What is potential energy dependent on?

What Is Potential Energy Dependent On?
What is potential energy dependent on? Image link: https://en.wikipedia.org/wiki/Nuclear_winter
C O N T E N T S:

KEY TOPICS

  • The sum of kinetic and potential energy in the system remains constant, assuming negligible losses to friction.(More…)
  • The potential energy of a mechanical object in relation to gravity is dependent on the mass of the object, and the height of the object above the earth.(More…)
  • Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well.(More…)
  • Since the total mechanical energy is conserved, kinetic energy (and thus, speed) will be greatest when the potential energy is smallest.(More…)

POSSIBLY USEFUL

  • The energy has been converted into kinetic energy–the energy of motion–but the process is not completely efficient and heat is also produced within the cyclist.(More…)
  • If you fix the composition, temperature, pressure, and phase of a homogeneous mass but change the volume, you will increase the amount of mass you included in the system, thus changing the total internal energy (because it is, after all, an extensive function).(More…)
  • For short sleepers (e.g., <4 h, Fig 3b ), the effect of state-dependent metabolic partitioning (MAI) on energy savings is strong compared to that of metabolic rate reduction during sleep.(More…)

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KEY TOPICS

The sum of kinetic and potential energy in the system remains constant, assuming negligible losses to friction. [1] When they start rising, the kinetic energy begins to be converted to gravitational potential energy. [1] They can be categorized in two main classes: potential energy and kinetic energy. [1] The work done on both of them is same (adding all the forces, including spring force on each other), which implies that the energy stored or potential energy is same. [2] Some springs are constant force (constant-force springs), so the expression for potential energy would not be a quadratic. [2] Spring potential energy depends upon the compression or elongation produced integral spring and the spring constant. [3] I was just willing to find a simple explanation (which does not involve equation) on why the potential energy of a spring is the same when stretched/compressed. [2] I’m giving a high school lecture and I want to introduce the potential energy of a spring. [2] Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy. [4] Potential energy is usually a function of the set of $x_i$ or position only. [5] The graph of a 2D potential energy function is a potential energy surface that can be imagined as the Earth’s surface in a landscape of hills and valleys. [4] A potential well is the region surrounding a local minimum of potential energy. [4] In quantum physics, potential energy may escape a potential well without added energy due to the probabilistic characteristics of quantum particles ; in these cases a particle may be imagined to tunnel through the walls of a potential well. [4]

Energy may be released from a potential well if sufficient energy is added to the system such that the local maximum is surmounted. [4]

The potential energy of a mechanical object in relation to gravity is dependent on the mass of the object, and the height of the object above the earth. [6] Potential energy is dependent on the object’s mass, its height (h) and the acceleration due to gravity (g). [7]

We find that the gauge invariant color singlet time dependent potential energy between static quarks does not violate the conservation of energy in the Yang-Mills theory. [8]

Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. [4] Kinetic energy is associated with the motion of a body, while potential energy is associated with its position or the state that it is in. [9] In order to do work, potential energy is converted into kinetic energy. [9] At times, there is a wrong notion prevalent that kinetic energy is considered to be actual energy as opposed to potential energy, which is considered to have the ‘potential’ of being actual energy. [9] A car driving down a mountain has kinetic energy from its movement and potential energy from its position relative to sea level. [10] When it is just about to hit the other balls, the potential energy has been converted to kinetic energy. [6] When the other ball goes up again, the kinetic energy turns, once more, into potential energy. [6]

If the object is placed above the ground, its potential energy is mgh, where m is the mass of the object, g is the gravitational constant, and h is the distance from the ground. If the object is a spring, it depends on how far it is streched or compressed.5kx 2, where k is the spring constant, and x is how much the spring has been compressed or stretched. There are many other forms of potential energy, but these two are probably the most common. [6] Potential energy can be calculated by the equation U ( which is the potential energy) mgh, where m is hte mass, g is gravity, and h is the height of the object above the point where h0 (often the ground). [6] The three things that determine gravitational potential energy are the strength of the gravitational field, the mass of the object on which it is acting, and its “altitude” or height of elevation in the field. There are some subtle complexities that also play a part in a complete dynamic picture, but these are the basics. [6] The potential energy of a body is directly proportional to its mass, height, and gravitational acceleration. [9] Gravitational potential energy (in the simplest case) is calculated as mgh (mass x gravity x height), so it depends on those three factors. [6] Gravitational potential energy depends on the weight of the objectand the height that the object is located at. [6] Just look at the formula: PE mgh potential energy mass x gravity x height So, it depends on those three things. [6] PE is potential energy, m is mass, g is acceleration due to gravity, and h is height. [10] Despite being at the same relative height, the potential energy of the three will vary, because of the different mass that they have. [9]

The basic physics concepts of kinetic and potential energy were described in terms relevant to the ocean in Section 7.7.5. [11] This post gives the explanation and differences between kinetic and potential energy, the two types of energy. [9] Although there are several types of energy, scientists can group them into two main categories: kinetic energy and potential energy. [10] As a pendulum swings, it has maximum potential energy at the top of the arc, yet zero kinetic energy. [10] At the bottom of the arc, it has no potential energy, yet maximum kinetic energy. [10] According to Albert Einstein’s Theory of Relativity, each particle of matter has inherent potential energy proportional to the particle’s mass and the square of the speed of light (c). [7] Potential energy of a body with certain mass is proportional to the vertical position of the body with respect to the ground. [6] The gravitational attraction that acts on a body is the reason for the body to possess potential energy. [9] Gravitational Potential energy -GmM/r, depends on three things; the product of the masses and inversely on the separation between the masses, r and finally the gravitational constant, G. [6] We present a new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schringer equation required to compute (ro-)vibrational spectra, photodissociation cross sections, reaction rate constants, etc., that can be used with general potential energy surfaces. [12] In this paper we show that the gauge invariant color singlet potential energy between static quarks in the classical Yang-Mills theory depends on time even if the quarks are at rest. [8] Potential energy that depends on height is called gravitationalpotential. [6] Potential energy (gravitational potential energy, to be more precise) is simply the weight multiplied by the height. [6] Greater the height, more potential energy their is due to falling force of gravity. [6] Eddy potential energy is calculated using departures of instantaneous sea surface height and isopycnal heights from their mean values; currently satellite altimetry data are valuable for this, and in situ Argo profiling float data set will also be valuable after many more years of data are collected. [11] In more general systems than the particle system mentioned here, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device. [13] Because potential energy reflects the position of an object, it can have a negative sign. [10] Potential Energy is passive energy – for the time being it does nothing but it can cause action at any time, given the required triggering. [6] Abstract: Lattice QCD predicts that the potential energy between static quarks is independent of time. [8] Using an unstretched spring as a reference position, a stretched spring has potential energy. [6] That depends what type of potential energy you are talking about. [6] If you were to go further and then break down and atom, such as in fission, or fuse two atoms, then truly displays the potential energy in a single atom, because this energy can destroy whole cities. [6] As long as h does not equal zero (imagine the man sandin on a cliff above sea leve, which is h0) then he will have potential energy. [6] The potential energy is EP mgh where g is the gravitaional acceleration and h the elevation. [6] Sure, when the ball is in the highest position, it has a maximum amount of potential energy. [6] A ball placed on a table on the first floor of an apartment that has ten floors, on the fifth floor, and the tenth floor of the same building, will have potential energy. [9]

While classical mechanics classifies all energy as either kinetic or potential, there are other forms of energy. [10] The calculation of energy in electrical systems depends on the amount of current flowing through a conductor (I) in amperes, as well as on the electrical potential, or voltage (V), driving the current, in volts. [7] Abstract: We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. [14] Sometimes simply “potential energy”, and the “gravitational” part is implied. [6]

This is called its kinetic energy, and it is dependent on the square of the object’s velocity (v) as well as one half of its mass (m). [7]

Since the total mechanical energy is conserved, kinetic energy (and thus, speed) will be greatest when the potential energy is smallest. [15] The potential energy that is lost is transformed into kinetic energy. [15] A primary objective is to compare potential energy savings derived from state-dependent metabolic partitioning versus metabolic rate reduction. [16] The Coulomb repulsion between protons decreases faster with elongation than the surface tension increases, and the two are in balance at point B, which represents the height of the barrier to fission. (This point is called the ” saddle point ” because, in a three-dimensional view of the potential energy surface, the shape of the pass over the barrier resembles a saddle.) [17] Further discussion of the potential energy in fission is provided below. [17] The object will have a minimum gravitational potential energy at point ____. [15] It is sometimes called gravitational potential energy (PE). [18] Chemical bonds have some of the properties of mechanical springs, whose potential energy depends on the extent to which they are stretched or compressed. [19] Each atom-to-atom bond can be described by a potential energy diagram that shows how its energy changes with its length. [19] Figure 2: The potential energy as a function of elongation of a fissioning nucleus. [17] This mechanism of energy savings is in conflict with the known upregulation (compared to wake) of diverse functions during sleep and neglects a potential role in energy conservation for partitioning of biological operations by behavioral state. [16] We show that although state-dependent metabolic partitioning has a greater potential impact on total energy savings when cycling between sleep and wakefulness, small reductions in metabolic rate during sleep may augment energy savings beyond what is achievable from metabolic partitioning alone. [16]

Our model suggests that partitioning of operations conserves energy through efficiencies in resource utilization, a potential advantage for species influenced by the predictability of the Earth?s rotation and the daily cycling of its ecology. [16]

It is dependent on the mass of the fissioning nucleus and the excitation energy at which the fission occurs. [17] Comparing an organism to a machine, r W refers to the rate of energy deployed for “running” the machine (energy acquisition, predation avoidance and reproduction), whereas r B to “maintenance” and “upgrading” of the machine. r W and r B contribute to growth in biological requirements (BR) dependent on their rates (equation 1), but only r B is converted into BI (equation 2). [16] The capacity to produce this energy is dependent on both the available flow and the height from which it falls. [20] The distributions in mass, charge, and kinetic energy of the fragments have been found to be dependent on the fissioning species as well as on the excitation energy at which the fission act occurs. [17]

The total mechanical energy (i.e., the sum of the kinetic and potential energies) is everywhere the same whenever there are no external or nonconservative forces (such as friction or air resistance) doing work. [15] As a continuation of the theme of potential and kinetic energy, this lesson introduces the concepts of momentum, elastic and inelastic collisions. [18]

We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parametrization. [21] Our results show that, even when including the standard Gaussian nonlocality in optical potential, a significant energy dependence is required to describe elastic-scattering data. [21] Some large windy areas, particularly in rural parts of the High Plains and Rocky Mountains, have enormous potential for energy production, although they have been out of reach for development because of their distance from load centers. [22] Domestically, Mr. Trump has made energy a centerpiece of his efforts to strengthen our economy and create jobs, but he needs to do more than loosen restrictions on oil and gas production: Many non-energy policies of the Trump administration undermine the energy boom and all its potential advantages. [23] The aggressive orientation of the Trump administration toward Mexico is also a potential problem for America?s energy sector and the pursuit of energy security. [23] Vibrational energy : the oscillatory motion of atoms or groups within a molecule (potential energy ? kinetic energy exchange). [24] Since the late 1990s, the DOE National Renewable Energy Laboratory (NREL) has been working with state governments to produce and validate high-resolution wind resource potential assessments on a state-by-state basis. [22]

POSSIBLY USEFUL

The energy has been converted into kinetic energy–the energy of motion–but the process is not completely efficient and heat is also produced within the cyclist. [1] William Thomson, later Lord Kelvin, is given credit for coining the term “kinetic energy,” around 1849-1851. [1]

The calculated value of this invariant mass compensates for changing energy in different frames, and is thus the same for all frames and observers. [1] What this suggests is that the formulas for energy and momentum are not special and axiomatic, but rather concepts which emerge from the equation of mass with energy and the principles of relativity. [1] The equation shows that the energy of an object approaches infinity as the velocity v approaches the speed of light c, thus it is impossible to accelerate an object across this boundary. [1]

Shown in the diagram is the change in electron energy level and bandgap between nanomaterial and its bulk state. [4] The terms energy level and energy state are often used loosely to mean quantum state. [25] Decreasing the volume or the dimensions of the available space, increases the energy of the states. [4] Spring energy is quadratic because increasing $d$ increases both the average force and the distance. [2] Finally the key point is that whether the spring is compressed or elongated, the force and the displacement have always the same (positive or negative) sign, therefore we always have positive work on the spring and positive energy stored in it. [2] In the case of frictional forces and inelastic systems, however, what we have is a time dependant Lagrangian, resulting in a time dependant energy and therefore dissipation. [5]

To do so I let them realize that stretching/compressing the spring will change its energy. [2] If they ask why the energy is the same in compression and tension, just say that there are springs for which this is not true. [2] My missing argument is therefore how to justify that the energy is the same when a spring is stretched/compressed by $d$. [2]

If you want to avoid calculus, give them a geometric understanding: plot the $F vs. x$ line and state that the energy is the area inbetween the x-axis and the curve. [2] During this state, the bandgap remains at its original energy due to a continuous energy state. [4] A rather good approximation of an exciton?s behaviour is the 3-D model of a particle in a box. 4 The solution of this problem provides a sole clarification needed mathematical connection between energy states and the dimension of space. [4]

Note that the energy is not destroyed; it has only been converted to another form by friction.) [1] Then by looking at the units of energy they should realize that the deformation $d$ has to be squared and that the constant $k$ takes care of the remaining units. [2] The translational kinetic energy depends on motion through space, and for a rigid body of constant mass is equal to the product of half the mass times the square of the speed. [25] In relativistic physics kinetic energy is equal to the product of the increase of mass caused by motion times the square of the speed of light. [25]

In any other frame of reference there is additional kinetic energy corresponding to the total mass moving at the speed of the center of mass. [1] The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass. [1] The total energy E can be partitioned into the energy of the rest mass plus the traditional Newtonian kinetic energy at low speeds. [1] In SI units (used for most modern scientific work), mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. [1] The kinetic energy of a system is lowest with respect to center of momentum reference frames, i.e., frames of reference in which the center of mass is stationary (either the center of mass frame or any other center of momentum frame). [1] Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer’s frame of reference. [1] The kinetic energy of systems of objects, however, may sometimes not be completely removable by simple choice of reference frame. [1] The total energy of the system (including kinetic energy, fuel chemical energy, heat energy, etc), will be conserved over time in a given reference frame, regardless of the choice of measurement frame. [1] The chemical energy converted to kinetic energy by a rocket engine will be divided differently between the rocket ship and its exhaust stream depending upon the chosen frame of reference. [1] The kinetic energy of any entity is relative to the frame of reference in which it is measured. [1]

The rotational kinetic energy depends on rotation about an axis, and for a body of constant moment of inertia is equal to the product of half the moment of inertia times the square of the angular velocity. [25] This equation states that the kinetic energy (E k ) is equal to the integral of the dot product of the velocity ( v ) of a body and the infinitesimal change of the body’s momentum ( p ). [1] Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. [1] At a low speed (v<<c), the relativistic kinetic energy may be approximated well by the classical kinetic energy. [1] Note that the kinetic energy increases with the square of the speed. [1] If the cue ball collides with another ball, it will slow down dramatically and the ball it collided with will accelerate to a speed as the kinetic energy is passed on to it. [1] If a body’s speed is a significant fraction of the speed of light, it is necessary to use relativistic mechanics (the theory of relativity as expounded by Albert Einstein ) to calculate its kinetic energy. [1] For a speed of 10km/s the correction to the Newtonian kinetic energy is 0.07 J/kg (on a Newtonian kinetic energy of 50 MJ/kg) and for a speed of 100km/s it is 710 J/kg (on a Newtonian kinetic energy of 5 GJ/kg), etc. [1]

This means, for example, that an object traveling twice as fast will have four times as much kinetic energy. [1] The kinetic energy of an object is the extra energy it possesses due to its motion. [1] There are several different equations that may be used to calculate the kinetic energy of an object. [1] Kinetic energy for single objects is completely frame-dependent (relative). [1]

The kinetic energy of a system at any instant in time is the sum of the kinetic energies of the bodies it contains. [1] The principle in classical mechanics that E ? mv was first theorized by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the “living force,” or vis viva. [1] The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. [1] Kinetic energy can be best understood by examples that demonstrate how it is transformed to and from other forms of energy. [1]

A bullet racing by a non-moving observer has kinetic energy in the reference frame of this observer, but the same bullet has zero kinetic energy in a reference frame that moves with the bullet. [1] A body that is stationary and not rotating nevertheless has internal energy, which is partly kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. [1] It is assumed that the body starts with no kinetic energy when it is at rest (motionless). [1]

This kinetic energy gained during launch will remain constant while in orbit because there is almost no friction. [1] The kinetic energy of flowing water or the wind can be used to move turbines, which in turn can be used to generate electricity. [1] The kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation. [1] In the game of billiards, the player gives kinetic energy to the cue ball by striking it with the cue stick. [1]

Spacecraft use chemical energy to take off and gain considerable kinetic energy to reach orbital velocity. [1] A cyclist will use chemical energy that was provided by food to accelerate a bicycle to a chosen speed. [1] There are various forms of energy, including chemical energy, heat, electromagnetic radiation, nuclear energy, and rest energy. [1]

@Gilbert Agreed – actually the contrary is the case, you can only compress a spring a small amount compared to the potential straight wire you might end up with by pulling (unless it breaks before). [2] Not the answer you’re looking for? Browse other questions tagged classical-mechanics forces lagrangian-formalism potential field-theory or ask your own question. [5] In the case of gravity, the region around a mass is a gravitational potential well, unless the density of the mass is so low that tidal forces from other masses are greater than the gravity of the body itself. [4] Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (e.g., be a lake ) without any water flowing away toward another, lower minimum (e.g. sea level ). [4]

If you fix the composition, temperature, pressure, and phase of a homogeneous mass but change the volume, you will increase the amount of mass you included in the system, thus changing the total internal energy (because it is, after all, an extensive function). [6] This energy, however, will not be the same in all the three cases, as even though the mass of the object remains the same, because its relative height keeps on varying. [9] Gravitationalpotential energy is the product of an objects weight and height. [6] An object in motion possesses its energy of movement, which is equivalent to the work that would be required to bring it to rest. [7] If you take a closed system and change the volume of it, you will be doing work (or allowing the system to do work) and the internal energy can change – so – yes – internal energy of a system depends upon volume. [6] On the mass and velocity also it depends on the mass and quickness.That is the type of energy that it depends on. [6]

This is the energy possessed by a body on account of its state or position. [9] It is generally true that the number of nodes increases with the energy of the quantum state, which can be rationalized by the following qualitative argument. [26] It is generally true in quantum systems (not just particles in boxes) that the number of nodes in a wavefunction increases with the energy of the quantum state. [26]

The state of lowest energy for a quantum system is termed its ground state. [26] The residual energy of the ground state, that is, the energy in excess of the classical minimum, is known as zero point energy. [26]

Energy is something that is at work everywhere around us all the time. [9] Work transfers energy from one place to another or one form to another. [13] This energy can be released in many different forms when a chemical reaction occurs or when the molecule is broken down. [6] One of the fundamental laws of the universe is that energy is neither created nor destroyed — it only changes forms. [7] In accordance to the ‘Law of Conservation of Energy’, energy can neither be created nor be destroyed; it can be converted from one form to another. [9] Here is a look at the forms of energy, with examples of each type. [10]

We test the collocation MCTDH equations we derive by showing that they can be used to compute accurate vibrational energy levels of CH 3. [12] EKE maps for deeper levels are calculated from Lagrangian float observations; moored current meter arrays are also used to calculated eddy energy locally. [11] The energy of an electron does vary depending on which energy level it occupies. [6] The integer \(n\), called a quantum number, is appended as a subscript on \(E\) to label the allowed energy levels. [26] The occurrence of discrete or quantized energy levels is characteristic of a bound system, that is, one confined to a finite region in space. [26]

It is also the energy required to bring a body in motion to rest. [9] Under statically unstable conditions with rising thermals, the largest eddies are strongly anisotropic, with much greater turbulent energy in the vertical motion component than in the horizontal component. [11] When the flow is statically stable but dynamically unstable, the vertical component of turbulence is partly suppressed by the negative buoyancy of the rising air and the positive buoyancy of the sinking air–a process referred to as buoyant consumption –resulting in anisotropy with moderate TKE in the horizontal motion component but very little energy in the vertical component. [11]

German physicist Max Planck determined that the energy of a photon is proportional the frequency (f) with which it vibrates, and he calculated the constant of proportionality (h), which is called Planck’s constant in his honor. [7] Energy is the capacity for doing work, and it is also expressed in joules. [7] Multiplying these two parameters gives the power of the electricity (P) in watts, and multiplying P by the time during which the electricity flows (t) in seconds gives the amount of electrical energy in the system, in joules. [7] Reducing the size of a molecule gives that molecule greaterpotential energy because the molecule isn’t using that energy sinceit is smaller. [6] A molecule of polysaccharide is made up of many sugars, or sacchride units. so a polysacchiride has more energy, because it has more sugars than a sugar alone. [6] Molecules actually have great amounts of energy within them. [6]

From the above equation, we can state that the kinetic energy of a body is directly proportional to its mass and squared value of its speed. [9] If m is mass in kg, and v is speed in m/s, then KE is kinetic energy in Joules. [6] The formula for the energy of motion is KE.5 m v 2 where KE is kinetic energy in joules, m is mass in kilograms and v is velocity in meters per second. [7] In meteorology we often use specific kinetic energy, namely KE / m, or the kinetic energy per unit mass. [11] Recall from basic physics that kinetic energy is K E 1 2 m V 2, where m is mass and V is velocity. [11]

The work-energy theorem states that the work done by all forces acting on a particle equals the change in the particle’s kinetic energy. [13] Kinetic energy can be termed as the energy to do work for accelerating a body from rest to the desired speed. [9] The kinetic energy of the block increases as a result by the amount of work. [13] Most work on lakes has focused solely on the influence of wind and largely has ignored the possibility of other sources of kinetic energy. [11] In temperate and arctic lakes, the overall depth of mixing in summer is reduced relative to tropical lakes for the same heat loss and flux of turbulent kinetic energy due to the greater work required to entrain the more stably stratified water below. [11] This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy. [13]

On a larger scale, any object in motion has kinetic energy. [10] A ball rolling on the floor has kinetic energy owing to its rolling motion. [9] A vehicle traveling on the road will possess kinetic energy on account of the motion that it is in. [9] Eddy kinetic energy from altimetry is often compared to that from drifters, with the difference attributed to wind-driven motion and smaller scales not resolved by altimetry. [11] In case of a system with multiple bodies, the kinetic energy possessed by them is due to the relative motion of the bodies present in it. [9] An asteroid that is falling also has kinetic energy that can be attributed to the falling motion. [9] Atoms and their components are in motion, so all matter possesses kinetic energy. [10]

The strongest eddies, such as Agulhas rings, propagate away from the mean flow that created them, accounting for broader EKE maxima compared with the speed (mean kinetic energy ) maxima. [11] This is equivalent to the amount of kinetic energy a 1-kilogram rock would have if you dropped it from a height of 612 meters (ignoring air friction). [7] XPS measures the kinetic energy distribution of electrons (photoelectrons) emitted from core levels of the elements constituting a solid when the sample is irradiated by X-rays ( Fig. 2.5.1 ). [11] Kinetic energy is further divided into various forms like rotational, translational, vibrational, etc., or also in combination. [9] Kinetic energy is transferred to water bodies by several means; most notable for gas exchange in lakes are wind shear and buoyancy flux. [11] Wind kinetic energy causes rotation of cup wheel or propeller anemometers. [11]

The higher the altitude of an object, the moregravitational potential the object has. [6] A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schringer equation with a general potential e. – PubMed – NCBI Warning: The NCBI web site requires JavaScript to function. more. [12] It is therefore not necessary to calculate potential values many times during the propagation. [12]

For short sleepers (e.g., <4 h, Fig 3b ), the effect of state-dependent metabolic partitioning (MAI) on energy savings is strong compared to that of metabolic rate reduction during sleep. [16] This interaction is consistent with the following proposition: State-dependent partitioning of metabolic processes is the primary mechanism of energy savings derived from sleep, whereas metabolic rate reduction the principle mechanism for torpor. [16] A combination of metabolic partitioning and metabolic rate reduction may enhance energy savings of sleep beyond what is achievable through metabolic partitioning alone ( Fig 3c ). [16] As a function of metabolic partitioning, our calculations show that coupling of metabolic operations with behavioral state may provide comparatively greater energy savings than the measured decrease in metabolic rate, suggesting that actual energy savings derived from sleep may be more than 4-fold greater than previous estimates. [16] Previous calculations of energy savings derived from sleep are based only on metabolic rate reduction, a mathematical calculation that implicitly assumes all metabolic functions to be equally reduced during sleep compared to wake. [16] Reductions in metabolic rate during the rest phase constrain MAI. Blue line is energy savings from ? (ES ? ), red line is savings from MAI (ES MAI ), and purple line is overall energy savings (ES MAI+? ). (D) Energy savings as a function of target MAI and circadian amplitude (A) with ? 0.3 and TST 8 h. [16] Applying the methodology used above, a comparison with Strategy Wake gives overall energy savings (ES MAI+? ) from both metabolic partitioning (MAI) and metabolic rate reduction (?). [16] Average metabolic rate over one 24 h day is then compared to Strategy Wake, giving energy savings from metabolic rate reduction (ES ? ). [16] Large increases in ?, however, are more compatible with the behavioral state of torpor where reducing metabolic rate is the primary mechanism of energy savings. [16] As a result of preferential coupling of unique biological functions with either sleep or wake, our calculations suggest that actual energy savings from sleep are potentially 4-fold greater than what was reported previously from metabolic rate reduction, theoretically reducing total energy requirements by over 50% for species with long sleep quotas (ES MAI+?, Fig 3b ). [16] Despite these constraints, energy savings from modest state-dependent metabolic partitioning equals or exceeds that from metabolic rate reduction across all sleep quotas ( Fig 3b ). [16] A mathematical model is presented to quantify the relative contributions of metabolic partitioning, metabolic rate reduction during sleep (rho: ?), sleep quota and the role of the circadian system in energy conservation. [16] The proposed interactions in our model between metabolic partitioning, metabolic rate reduction, sleep quota, and the circadian system are not intuitively obvious, but they provide testable hypotheses on the optimization of sleep or torpor strategies employed across species for energy conservation. [16]

Long sleeping endotherms are particularly prone to enter daily (nightly) torpor when challenged by energetic shortfalls, suggesting an adaptive capability to shift energy allocation strategies between primarily metabolic partitioning (sleep) or metabolic rate reduction (torpor) depending on energy status. [16] This current perspective views metabolic rate reduction during sleep as the mechanism of energy savings. [16] To illustrate, an 8 h metabolic rate reduction of 15-30% during sleep compared to quiet wakefulness results in a 5-15% decrease in total daily (24 h) energy expenditure, a finding often cited as only a “cup of milk” for an adult human. [16] Metabolic rate reduction has been considered the mechanism by which sleep conserves energy, similar to torpor or hibernation. [16] The model predicts that metabolic rate reduction is not required for sleep to conserve energy. [16] These interactions predict short sleeping species to maintain a relatively elevated metabolic rate during sleep to optimize energy conservation through metabolic partitioning, a prediction requiring further investigation. [16] Here we propose that actual energy savings from sleep may be more than 4-fold greater than previous estimates, primarily reflecting the contribution from state-dependent metabolic partitioning. [16] Citation: Schmidt MH, Swang TW, Hamilton IM, Best JA (2017) State-dependent metabolic partitioning and energy conservation: A theoretical framework for understanding the function of sleep. [16] Experimental work is required to assess the role of coupling specific biological functions with either rapid eye movement (REM) or non-REM sleep to further exploit metabolic partitioning for energy conservation in endotherms as the energy allocation hypothesis postulates. [16] These data are consistent with a state-dependent metabolic partitioning as outlined in the recently proposed energy allocation hypothesis of sleep. [16] Using the method demonstrated in Fig 2, continuous wakefulness is used as the comparator state for computations of energy savings derived from sleep. [16] Monitoring of biological debt, while normalizing meaningful comparisons of energy savings calculations across strategies, demonstrates a well-defined temporal pattern that we postulate may impact sleep regulation. [16] The energy allocation model defines four variables that may impact energy savings derived from sleep. [16] These previous observations, often employing short-term sleep restriction, are not designed to determine differences in net energy savings between habitual continuous wakefulness and habitual sleep-wake cycling. [16] We conclude that the upregulation of central and peripheral biological processes during sleep is driven by the evolutionary selective advantage of partitioning metabolic operations, the principal mechanism by which sleep optimizes energy conservation across species. [16] The energy allocation model also ascribes an important role for the circadian system in energy conservation when combined with at least a modest partitioning of metabolic operations by behavioral state ( Fig 3d ). [16]

In order to effectively initiate a reaction, collisions must be sufficiently energetic (kinetic energy) to bring about this bond disruption. [19] As the excitation energy of the fission increases, the probability for a symmetric mass split increases, while that for asymmetric division decreases. [17] At low excitation energy, the fission of such nuclides as uranium-235 or plutonium-239 is asymmetric; i.e., the fragments are formed in a two-humped probability (or yield) distribution favouring an unequal division in mass. [17] Figure 5: Mass distribution dependence on the energy excitation in the fission of uranium-235. [17] The conversion of mass to energy follows Einstein?s equation, E m c 2, where E is the energy equivalent of a mass, m, and c is the velocity of light. [17] The energy equivalent of this mass difference is given by the Einstein relation, E m c 2. [17]

As shown in Fig 3a, maximizing MAI amplifies energy savings by approximately 4-fold over the alternative strategy of continuous wakefulness ( Fig 3a ), resulting in total energy savings of ~37% for an 8 h sleep quota. [16] Gains in energy savings are primarily derived from MAI for TST<7 h or from ? as TST exceeds 14 h. (C) Varying ? with target MAI 0.7 and TST 8 h. [16] Energy savings from ? and MAI may then be computed in the following manner: 1) Energy savings from ? is ES ? ( m MR 1 ? m MR 2 )/ m MR 1, 2) overall energy savings from MAI and ? is ES MAI+ ? ( m MR 1 ? m MR 3 )/ m MR 1, and 3) energy savings from MAI is ES MAI ES MAI+ ? ? ES ?. [16] While calculating energy savings, we attempt to reach a target MAI of 0.6 with ? 0.3. [16] Energy savings is computed at this stage; here, ES MAI+ ? ? 28%. (Parameters: TST 8 h, r Ww 0.5, r Bw 0.3, r Ws 0.126, r Bs 0.434). [16] If instead, the green line is below the red line at the bifurcation point, we compute energy savings at that point. (Parameters: TST 8 h, r Ww 0.5, r Bw 0.20079, r Ws 0.15378, r Bs 0.33678). (D) Strategy MP + MR Reduction, two fixed points of Poincarmap. [16] To compute energy savings, we compare three strategies: Strategy Wake, Strategy MR Reduction, and Strategy metabolic partitioning (MP) + MR Reduction. [16]

In order to compute energy savings, we must find the four energy rates ( r Ww, r Bw, r Ws, r Bs ) subject to conditions that are strategy-dependent. [16] The MAI is quantified using the relative rates of energy deployment for biological functions directed toward either waking effort (r W ) or biological investment (r B ). [16] Note that MAI 0 means that the energy allocations are the same in both wake and sleep (i.e. ), while MAI 1 implies r Bw r Ws 0. [16] The circadian process, C ( t ), participates as an efficiency multiplier in the conversion of energy ( r B ) to BI, providing greater efficiency during the sleep phase and less during the wake phase. [16] A mathematical model is presented based on relative rates of energy deployment for biological processes upregulated during either wake or sleep. [16] To find values for the energy rates that will equalize m BD between Strategy Wake and the other strategies, we adjust r Bw starting at r Bw 0 and increase it until we reach the same m BD as in Strategy Wake. [16] Comparing an organism to a machine, r W refers to the rate of energy deployed for “running” the machine (energy acquisition, predation avoidance and reproduction), whereas r B to “maintenance” and “upgrading” of the machine. [16] S1 Fig. Energy allocation and MAI. r W is the dashed red line, r B is dot-dashed blue line, and MR is solid purple line. [16] Performing all processes simultaneously (MAI 0) theoretically increases cellular infrastructure requirements, an additional energy cost not addressed in the model. [16] We hypothesize that such whole organism partitioning potentially increases energy savings beyond what a single organ system could otherwise achieve. [16] Long-sleeping species, in contrast, should more likely reduce metabolic rate during sleep given its increasing gains toward energy savings as sleep quota approaches 24 h. [16] Sleep quota and the circadian system further augment energy savings in the model. [16] Sleep quota and the circadian system further enhance energy conservation in the model. [16] Energy conservation from sleep quota and the circadian system are also quantified in relation to a continuous wake condition. [16] We also identify an interaction between the circadian system and state-dependent metabolic partitioning in energy conservation. [16] This latter effect results from inefficiencies in expending energy on state-dependent processes when comparatively out of phase with the circadian system. [16] Energy savings as derived from state-dependent resource allocations have yet to be examined. [16] Surprisingly, there are no published reports on energy savings derived from coupling biological processes with behavioral state. [16] Using this model, energy savings from sleep-wake cycling over constant wakefulness is computed by comparing stable limit cycles for systems of differential equations. [16] Varying m C in addition to p W and p B 1 accounts for a total range of energy savings of less than 8%. [16] At any given value of m C, varying p W and p B 1 over a wide range of values accounts for only a 1-4% change in energy savings. [16] In addition to quantifying the relative contributions of these variables in energy conservation, the model also identifies for the first time specific interactions between these variables potentially impacting energy savings. [16] The current energy conservation hypothesis has been criticized as providing only limited energy savings. [16] When computing energy savings, we attempt to keep average BD the same for each strategy. [16] S3 Fig. Low sensitivity of parameters p W, p B 1, and m C was observed for energy savings calculations. [16] Each box-and-whisker plot has a different fixed value of m C, with values of energy savings resulting from varying p W and p B 1 from 0 to 2 in intervals of 0.1 (if the system has a limit cycle). [16]

The second efficiency multiplier component of x B ( t ) depends on the level of BD to model a reactive homeostasis in the conversion of energy to BI. The curve of this reactive homeostatic component is low at low levels of BD, peaks at some moderate level of BD, and decreases asymptotically to 0 as BD increases; this shape reflects greatest efficiency in energy conversion at some moderate level of BD but with decreasing efficiency at either low or high levels of BD. [16] As the energy of fission increases, the charge division tends toward maintaining the n / p ratio in the fragments the same as that in the fissioning nucleus. [17] A fissionable system (uranium-238, for example) in its ground state (i.e., at its lowest excitation energy and with an elongation small enough that it is confined inside the fission barrier) has a small but finite probability of being in the energetically favoured configuration of two fission fragments. [17] The total energy release in a fission event may be calculated from the difference in the rest masses of the reactants (e.g., 235 U + n ) and the final stable products (e.g., 93 Nb + 141 Pr + 2 n ). [17] As the nucleus of the fragment adjusts from its deformed shape to a more stable configuration, the deformation energy (i.e., the energy required to deform it) is recovered and converted into internal excitation energy, and neutrons and prompt gamma rays (an energetic form of electromagnetic radiation given off nearly coincident with the fission event) may be evaporated from the moving fragment. [17] Although the heavy elements are unstable with respect to fission, the reaction takes place to an appreciable extent only if sufficient energy of activation is available to surmount the fission barrier. [17] In the fission process, a large quantity of energy is released, radioactive products are formed, and several neutrons are emitted. [17] These neutrons can induce fission in a nearby nucleus of fissionable material and release more neutrons that can repeat the sequence, causing a chain reaction in which a large number of nuclei undergo fission and an enormous amount of energy is released. [17] Armed with the unequivocal results of Hahn and Strassmann, however, Meitner and Frisch invoked the recently formulated liquid-drop model of the nucleus to give a qualitative theoretical interpretation of the fission process and called attention to the large energy release that should accompany it. [17] The more abundant isotope uranium-238 could be made to undergo fission only by fast neutrons with energy exceeding 1 MeV. The nuclei of other heavy elements, such as thorium and protactinium, also were shown to be fissionable with fast neutrons; and other particles, such as fast protons, deuterons, and alphas, along with gamma rays, proved to be effective in inducing the reaction. [17] Fission can be induced by exciting the nucleus to an energy equal to or greater than that of the barrier. [17] Fission is the breakup of a heavy nucleus (either spontaneously or under the impact, for example, of a neutron) into two smaller ones with liberation of energy and neutrons. [17] This “pairing energy” accounts in part for the difference in behaviour of nuclides in which fission can be induced with slow (low-energy) neutrons and those that require fast (higher-energy) neutrons. [17] There is a delayed release of energy from the radioactive decay of the fission products varying in half-life from fractions of a second to many years. [17] Overall, about 200 MeV of energy per fission may be recovered for power applications. [17]

Zepelin H, Rechtschaffen A. Mammalian sleep, longevity, and energy metabolism. [16] Schmidt MH. The energy allocation function of sleep: a unifying theory of sleep, torpor, and continuous wakefulness. [16] Sleep has long been considered an energy conservation strategy similar to torpor or hibernation. [16] Other processes are instead upregulated in wakefulness and downregulated in sleep, including excitatory neurotransmission, energy metabolism and responses to cellular stress. [16] Jung CM, Melanson EL, Frydendall EJ, Perreault L, Eckel RH, Wright KP. Energy expenditure during sleep, sleep deprivation and sleep following sleep deprivation in adult humans. [16]

Note that these equations are defined so that all energy rates are positive. [16] When the dynamical equation is solved without this approximation, the T -matrix has only one pole in the energy region of the \(\Lambda (1405)\) resonance. [27]

Lesson 2 has thus far focused on how to analyze motion situations using the work and energy relationship. [15] Thermal energy relates direction to motion at the molecular level. [19] Break the cycle of dirty energy money, particularly by elected officials at all levels of government pledging to refuse campaign donations and other forms of support from the oil, gas, and coal industries. [28] The energy requirements to maintain comparable levels of biological debt when restricting sleep-dependent processes have not been considered. [16]

Although most energy in the United States is produced by fossil-fuel and nuclear power plants, hydroelectricity is still important to the Nation. [20] China is the largest producer of hydroelectricity, followed by Canada, Brazil, and the United States (Source: Energy Information Administration ). [20] These states may differ by their allocations of energy to processes according to the strategy employed. [16] When the bond absorbs energy (either from heating or through a collision), it is elevated to a higher quantized vibrational state (indicated by the horizontal lines) that weakens the bond as its length oscillates between the extended limits corresponding to the curve. [19]

Hydropower represents about 17% ( International Energy Agency ) of total electricity production. [20] This energy is released on a time scale of about 10 -12 second and is called the prompt energy release. [17] The number of neutrons emitted from each fragment depends on the amount of energy the fragment possesses. [17] The energy can be in the form of internal excitation (heat) energy or stored as energy of deformation of the fragment to be released when the fragment returns to its stable equilibrium shape. [17] Gather, analyze, and interpret data to describe the different forms of energy and energy transfer (Grade 8) Details. [18]

Based upon the types of forces acting upon the system and their classification as internal or external forces, is energy conserved? Explain. [15] Hydroelectric energy is produced by the force of falling water. [20]

A combination of characteristics makes an airbag a good safety device; using up energy to deform the bag instead of the driver’s body is one of them. [18] Within about 10 -13 second this excitation gets distributed among the other bonds in the molecule in rather complex and unpredictable ways that can concentrate the added energy at a particularly vulnerable point. [19] Although the C-C bonds in cyclopropane are all identicial, the instantaneous localization of the collisional energy can distort the molecule in various ways ( ), leading to a configuration sufficiently unstable to initiate the rearrangement to the product. [19] Most reactions involving neutral molecules cannot take place at all until they have acquired the energy needed to stretch, bend, or otherwise distort one or more bonds. [19]

Indicate whether the energy of the ball is conserved and explain why. [15] All the energy goes into deforming the ball into a flat blob. [18] Momentum and energy loss of balls colliding against different surfaces: http://www.iit.edu/smile/ph8709.html. [18]

Renewable resources including hydropower, wind, biomass and solar energy are also used to produce electricity, but often on a smaller scale. [29] Oil Change International campaigns to expose the true costs of fossil fuels and facilitate the coming transition towards clean energy. [28]

The total kinetic energy of the system (which includes the objects that collide) is the same before and after the collision. [18] Kinetic energy is the energy an object has because of its motion ; any object that is moving has kinetic energy. [18] Therefore, the object will have less kinetic energy at point C than at point B (only). [15] The object gains _____ Joules of kinetic energy during this interval. [15] The answers given here for the speed values are presuming that all the kinetic energy of the ball is in the form of translational kinetic energy. [15] At impact, the cue ball stops, but transfers all of its momentum and kinetic energy to the other ball, resulting in the hit ball rolling with the initial speed of the cue ball. [18] The actual speed values would be slightly less than those indicated. (Rotational kinetic energy is not discussed here at The Physics Classroom Tutorial.) [15]

It is clear from these plots that the fraction of molecules whose kinetic energy exceeds the activation energy increases quite rapidly as the temperature is raised. [19] A is the fraction of molecules that would react if either the activation energy were zero, or if the kinetic energy of all molecules exceeded E a — admittedly, an uncommon scenario. [19] In the vast majority of cases, we depend on thermal actvation, so the major factor we need to consider is what fraction of the molecules possess enough kinetic energy to react at a given temperature. [19] Recall that the exponential part of the Arrhenius equation expresses the fraction of reactant molecules that possess enough kinetic energy to react, as governed by the Maxwell-Boltzmann law. [19]

In an inelastic collision, momentum is conserved, but the total kinetic energy of the system is not conserved. [18] In actuality, some of the kinetic energy would be in the form of rotational kinetic energy. [15] Additional energy must then be supplied in the form of the kinetic energy of the incident neutron. (In the case of thorium-232 or uranium-238, a neutron having about 1 MeV of kinetic energy is required.) [17]

The antineutrinos that accompany the beta decay of the fission products are unreactive, and their kinetic energy (about 10 MeV per fission) is not recovered. [17] The enormous energy released in a fission reaction appears primarily as the kinetic energy of the two fission products. [17]

What is the significance of this quantity? If you recall that RT is the average kinetic energy, it will be apparent that the exponent is just the ratio of the activation energy E a   to the average kinetic energy. [19] In an article on the Kinetics of Popping of Popcorn ( Cereal Chemisty 82(1): 53-59 ), J. Byrd and M. Perona found that popping follows a first-order rate law with an activation energy of 53.8 kJ/mol. [19]

As the object moves from point A to point D across the surface, the sum of its gravitational potential and kinetic energies ____. [15] The potential of nuclear fission for good or evil and the risk/benefit ratio of its applications have not only provided the basis of many sociological, political, economic, and scientific advances but grave concerns as well. [17] Molecules capable of losing or gaining electrons at the surface of an electrode can undergo activation from an extra potential (known as the overvoltage ) between the electrode and the solution. [19]

The above methodology demonstrates that a 30% reduction in metabolic rate (? 0.3) for 8 h of sleep with MAI 0 provides a 7.5% daily energy savings (ES ? ) over Strategy Wake ( Fig 3a ). [16] As demonstrated in Fig 3c, an 8 h sleep quota with a target MAI 0.7 provides a calculated daily energy savings of 35% without reducing metabolic rate (? 0). [16]

Daily energy savings are reduced when circadian amplitude is increased in the absence of state-dependent metabolic partitioning (i.e., MAI 0). [16] The upregulation of these diverse functions during sleep is viewed to be in the service of state-dependent metabolic partitioning, a mechanism by which daily energy conservation is optimized. [16] Given the calculated impact of sleep-wake cycling on reducing daily energy requirements, we propose that the ultimate (evolutionary) function of sleep is energy conservation through a state-dependent coupling of biological operations. [16] This new paradigm postulates that state-dependent coupling of biological functions partitions energy resources in a manner that provides comparatively greater daily energy conservation than metabolic rate reduction. [16] We propose that state-dependent resource allocation underpins both sleep homeostasis and the optimization of daily energy conservation across species. [16] Prior work suggested that 8 h of sleep only reduces daily energy expenditures by 5-15%. [16]

Whenever work is done upon an object by an external or nonconservative force, there will be a change in the total mechanical energy of the object. [15] If only internal forces are doing work (no work done by external forces), there is no change in total mechanical energy; the total mechanical energy is said to be “conserved.” [15]

Since it does work, the total mechanical energy is not conserved. [15] Since it is an internal or conservative force, the total mechanical energy is conserved. [15] Whatever total mechanical energy (TME) it has initially, it will maintain throughout the course of its motion. [15]

This difference is known as the mass defect and is a measure of the total binding energy (and, hence, the stability) of the nucleus. [17] A curve illustrating the average binding energy per nucleon as a function of the nuclear mass number is shown in Figure 1. [17] Figure 1 indicates that any nucleus heavier than mass number 56 would become a more stable system by breaking into lighter nuclei of higher binding energy, the difference in binding energy being released in the process. (It should be noted that nuclei lighter than mass number 56 can gain in stability by fusing to produce a heavier nucleus of greater mass defect–again, with the release of the energy equivalent of the mass difference. [17] The largest binding energy (highest stability) occurs near mass number 56–the mass region of the element iron. [17]

Radium isotopes show interesting triple-humped mass distributions, and nuclides lighter than radium show a single-humped, symmetric mass distribution. (These nuclides, however, require a relatively high activation energy to undergo fission.) [17] High temperature and low activation energy favor larger rate constants, and thus speed up the reaction. [19] What would limit the rate constant if there were no activation energy requirements? The most obvious factor would be the rate at which reactant molecules come into contact. [19] The two plots below show the effects of the activation energy (denoted here by E ‡ ) on the rate constant. [19]

Even a modest activation energy of 50 kJ/mol reduces the rate by a factor of 10 8. [19]

Activation energy diagrams always incorporate the energetics (Δ U or Δ H ) of the net reaction, but it is important to understand that the latter quantities depend solely on the thermodynamics of the process which are always independent of the reaction pathway. [19] The activated complex (also known as the transition state ) represents the structure of the system as it exists at the peak of the activation energy curve. [19] Define catalyst, and sketch out an activation energy diagram that illustrates how catalysts work. [19] There is a relationship between work and mechanical energy change. [15] Friction would do negative work and thus remove mechanical energy from the falling ball. [15]

Government giveaways in the form of permanent tax breaks to the fossil fuel industry – one of which is over a century old – are seven times larger than those to the renewable energy sector. [28] As products are formed, the activation energy is returned in the form of vibrational energy which is quickly degraded to heat. [19] Activation energy diagrams of the kind shown below plot the total energy input to a reaction system as it proceeds from reactants to products. [19] In most cases, the activation energy is supplied by thermal energy, either through intermoleculr collisions or (in the case of thermal dissocation) by thermal excitation of a bond-stretching vibration to a sufficiently high quantum level. [19] We have been neglecting it because it is not directly involved in relating temperature and activation energy, which is the main practical use of the equation. [19] It’s not enough that the wavelength of the light correspond to the activation energy; it must also fall within the absorption spectrum of the molecule, and (in a complex molecule) enough of it must end up in the right part of the molecule, such as in a particular bond. [19] This affords a simple way of determining the activation energy from values of k observed at different temperatures; we just plot ln k as a function of 1/ T. [19]

If a neutron is added to a nucleus having an odd number of neutrons, an even number of neutrons will result, and the binding energy will be greater than for the addition of a neutron that makes the total number of neutrons odd. [17] The binding energy of a particular nucleon to a nucleus will depend on–in addition to the factors considered above–the odd-even character of the nucleus. [17] The addition of a neutron in the former case liberates sufficient binding energy to induce fission. [17] The binding energy is less and may be insufficient to surmount the barrier and induce fission. [17] A few of the fission products have beta-decay energies that exceed the binding energy of a neutron in the daughter nucleus. [17]

Our calculations suggest that daily energy requirements would be much greater for organisms to achieve habitual, long-term, continuous wakefulness while maintaining comparable levels of biological debt with respect to an alternative sleep-wake cycling strategy. [16] If all biological processes are to be performed simultaneously without interruption (i.e., MAI 0), the optimal strategy reducing daily energy expenditures is to dampen or eliminate circadian amplitude. [16]

As described in Fig 1, both r W and r B contribute to growth in biological requirements dependent on their rates, but only r B is converted to biological investment. [16] The speed at the bottom of the incline is dependent upon the initial height of the incline. [15] The height and shape of the fission barrier are dependent on the particular nucleus being considered. [17]

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