Cantorian-Fractal Kinetic Energy and Potential Energy as the Ordinary and Dark Energy Density of the Cosmos Respectively

In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.

Gedanken Experiment Examining How Kinetic Energy Would Dominate Potential Energy, in Pre-Planckian Space-Time Physics, and Allow Us to Avoid the BICEP 2 Mistake

We use Padmabhan’s “Invitation to Astrophysics” formalism of a scalar field evolution of the early universe, from first principles, to show something which seems counter intuitive. How could, just before inflation, kinetic energy be larger than potential energy in pre-Planckian physics, and what physics mechanism is responsible for the Planckian physics result that Potential energy is far larger than kinetic energy. This document answers that question, as well as provides a mechanism for the dominance of kinetic energy in pre-Planckian space-time, as well as its reversal in the Planckian era of cosmology. The kinetic energy is proportional to , with initial degrees of freedom, and T the initial temperature just before the onset of inflation. Our key assumption is the smallness of curvature, as given in the first equation, which permits adoption of the Potential energy and Kinetic energy formalism used, in the Planckian and pre-Planckian space-time physics. Interpretation of this result, if done correctly, will be able to allow a correct distinguishing of relic gravitational waves, as to avoid the BICEP 2 pickup of galactic dust as a false relic Gravitational wave signal, as well as serve as an investigative template as to if quantum gravity is embedded in a deterministic dissipative system, as cited in the conclusion.

Kinetic Energy Budget Equations of Rotational and Divergent Flow in Terrain-following Coordinates

In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be applied directly to model-simulated dynamic and thermodynamic fields on the model's original vertical grid. Such application eliminates interpolation error and avoids errors in virtual weather systems in mountainous areas. These advantages and their significance are demonstrated by a numerical study in terrain-following coordinates of a developing vortex after it moves over the Tibetan Plateau in China.

DOMINANT PHYSICAL PROCESSES ASSOCIATED WITH PHASE DIFFERENCES BETWEEN SURFACE RAINFALL AND CONVECTIVE AVAILABLE POTENTIAL ENERGY

A lag correlation analysis is conducted with a 21-day TOGA COARE cloud-resolving model simulation data to identify the phase relation between surface rainfall and convective available potential energy (CAPE) and associated physical processes. The analysis shows that the maximum negative lag correlations between the model domain mean CAPE and rainfall occurs around lag hour 6. The minimum mean CAPE lags mean and convective rainfall through the vapor condensation and depositions,water vapor convergence,and heat divergence whereas it lags stratiform rainfall via the transport of hydrometeor concentration from convective regions to raining stratiform regions,vapor condensation and depositions,water vapor storage,and heat divergence over raining stratiform regions.

Previously Unknown Formulas for the Relativistic Kinetic Energy of an Electron in a Hydrogen Atom

Einstein’s energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein’s relationship is not applicable in a hydrogen atom, where potential energy is present. However, a relationship similar to that can be derived. That derived relationship also contains two formulas, for the relativistic kinetic energy of an electron in a hydrogen atom. Furthermore, it is possible to derive a third formula for the relativistic kinetic energy of an electron from that relationship. Next, the paper looks at the fact that the electron has a wave nature. Five more formulas can be derived based on considerations relating to the phase velocity and group velocity of the electron. This paper presents eight formulas for the relativistic kinetic energy of an electron in a hydrogen atom.

Quantization of the Kinetic Energy of Deterministic Chaos

In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic scalar dynamic structures, and the theoretical and experimental deterministic vector dynamic structures have been developed to compute the exact solution for deterministic chaos of the exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. To explore properties of the kinetic energy, rectangular, diagonal, and triangular summations of a matrix of the kinetic energy and general terms of various sums have been used in the current paper to develop quantization of the kinetic energy of deterministic chaos. Nested structures of a cumulative energy pulson, an energy pulson of propagation, an internal energy oscillon, a diagonal energy oscillon, and an external energy oscillon have been established. In turn, the energy pulsons and oscillons include group pulsons of propagation, internal group oscillons, diagonal group oscillons, and external group oscillons. Sequentially, the group pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons, diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons and oscillons are composed of elementary pulsons of propagation, internal elementary oscillons, diagonal elementary oscillons, and external elementary oscillons. Topology, periodicity, and integral properties of the exponential pulsons and oscillons have been studied using the novel method of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time. Symbolic computations of the exact expansions have been performed using the experimental and theoretical programming in Maple. Results of the symbolic computations have been justified by probe visualizations.

Generalized Available Potential Energy

The kinetic energy generation in either the dry or moist atmosphere may be estimated by the same relationships if we introduce the new concept of generalized available potential energy. The largest magnitude of generalized available potential energy and corresponding reference state of either dry or moist atmosphere are calculated in terms of the mitial conditions and entropy variation of the atmosphere. The obtained relationships are applicable for the statically unstable atmosphere as well. The generalized available potential energy associated with reversible processes reaches the maximum with respect to same initial state. While the generation of kinetic energy in irreversible processes is characterized by sudden changes. When the reference state is assumed to be saturated, we may predict the final temperature and moisture fields corresponding to provided initial state and entropy variation.

Surface available gravitational potential energy in the world oceans

Satellite altimetry observations,including the upcoming Surface Water and Ocean Topography mission,provide snapshots of the global sea surface high anomaly field.The common practice in analyzing these surface elevation data is to convert them into surface velocity based on the geostrophic approximation.With increasing horizontal resolution in satellite observations,sea surface elevation data will contain many dynamical signals other than the geostrophic velocity.A new physical quantity,the available surface potential energy,is conceptually introduced in this study defined as the density multiplied by half of the squared deviation from the local mean reference surface elevation.This gravitational potential energy is an intrinsic property of the sea surface height field and it is an important component of ocean circulation energetics,especially near the sea surface.In connection with other energetic terms,this new variable may help us better understand the dynamics of oceanic circulation,in particular the processes in connection with the free surface data collected through satellite altimetry.The preliminary application of this concept to the numerically generated monthly mean Global Ocean Data Assimilation System data and Archiving,Validation,and Interpretation of Satellite Oceanographic altimeter data shows that the available surface potential energy is potentially linked to other dynamic variables,such as the total kinetic energy,eddy kinetic energy and available potential energy.

Nonlinear dynamics and performance analysis of modified snap-through vibration energy harvester with time-varying potential function

Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example,the snap-through VEH with geometric non-linearity,has gained attention in recent years.A conventional snap-through VEH is a bi-stable system with a time-invariant potential function,which was investigated extensively in the past.In this work,a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated.Modified snap-through VEHs,such as the one considered in this study,are used in wave energy harvesters.However,the studies on their dynamics and energy harvesting under harmonic and random excitations are limited.The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations(DAEs),and the numerical schemes are proposed for its solutions.Under a harmonic excitation,the system exhibits periodic and chaotic motions,and the energy harvesting is superior compared with the conventional counterpart.The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method.The Fokker-Planck equation representing the dynamics is derived,and the marginal and joint probability density functions(PDFs)are obtained by the Monte Carlo simulation.The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations.The dynamics of the system under stochastic resonance(SR)is investigated,and performance enhancement is observed.The results from this study will help in the development of adaptive VEH techniques in the future.

A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Insufficiency of Cellular Energy (ICE) May Precede Neurodegeneration in Alzheimer’s Disease and Be Treatable via the Alternative Cellular Energy (ACE) Pathway

The term neurodegeneration emphasizes the destruction of neuronal cells as the primary explanation of many major neurological illnesses, including Alzheimer’s disease. Specialized functioning of cells requires more cellular energy than is needed for basic cell survival. Cells can acquire energy both from the metabolism of food and from the alternative cellular energy (ACE) pathway. The ACE pathway is an added dynamic (kinetic) quality of the body’s fluids occurring from the absorption of an external force termed KELEA (Kinetic Energy Limiting Electrostatic Attraction). KELEA is attracted to separated electrical charges and is seemingly partially released as the charges become more closely linked. As suggested elsewhere, the fluctuating electrical activity in the brain may attract KELEA from the environment and, thereby, contribute to the body’s ACE pathway. Certain illnesses affecting the brain may impede this proposed antenna function of the brain, leading to a systemic insufficiency of cellular energy (ICE). Furthermore, individual neurons may derive some of the energy for their own activities from the repetitive depolarization of the cell. This may explain why hyper-excitability of neurons can occur in response to cell damage. This adaptive mechanism is unlikely to be sustainable, however, especially if there is a continuing need to synthesize neurotransmitters and membrane ion channels. The energy deficient neurons would then become quiescent and, although remaining viable, would not perform their intended specialized functions. Actual cell death would not necessarily occur till much later in the disease process. The distinction between quiescent and degenerated cells is important since the ACE pathway can be enhanced by several means, including the regular consumption of KELEA activated water. This, in turn, may improve the proposed antenna function of individual neurons, leading to a sustained restoration of specialized function via the ACE pathway. This paper explores this novel concept and provides a rationale for clinical testing of KELEA activated water in patients with neurological and psychiatric illnesses, including Alzheimer’s disease.

Assessment of wind energy potential in China

China wind atlas was made by numerical simulation and the wind energy potential in China was calculated. The model system for wind energy resource assessment was set up based on Canadian Wind Energy Simulating Toolkit (WEST) and the simulating method was as follows. First, the weather classes were obtained depend on meteorological data of 30 years. Then, driven by the initial meteorological field produced by each weather class, the meso-scale model ran for the distribution of wind energy resources according each weather class condition one by one. Finally, averaging all the modeling output weighted by the occurrence frequency of each weather class, the annual mean distribution of wind energy resources was worked out. Compared the simulated wind energy potential with other results from several activities and studies for wind energy resource assessment, it is found that the simulated wind energy potential in mainland of China is 3 times that from the second and the third investigations for wind energy resources by CMA, and is similar to the wind energy potential obtained by NREL in Solar and Wind Energy Resource Assessment(SWERA) project. The simulated offshore wind energy potential of China seems smaller than the true value. According to the simulated results of CMA and considering lots of limited factors to wind energy development, the final conclusion can be obtained that the wind energy availability in China is 700～1 200 GW, in which 600～1 000 GW is in mainland and 100～200 GW is on offshore, and wind power will become the important part of energy composition in future.

Thermodynamic Equilibrium of the Saturated Fluid with a Free Surface Area and the Internal Energy as a Function of the Phase-Specific Volumes and Vapor Pressure

This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.

Photon Structure and Wave Function from the Vector Potential Quantization

A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.

The Incompleteness of Quantum Mechanics Demonstrated by Considerations of Relativistic Kinetic Energy

The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is because the classical quantum theory of Bohr does not take the theory of relativity into account. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are treated relativistically. A clearer argument is developed while also referring to papers published in the past. The energy levels of a hydrogen atom predicted by this paper almost match the theoretical values of Bohr. It is difficult to experimentally distinguish the two. However, this paper predicts the existence of an n = 0 energy level that cannot be predicted even with Dirac’s relativistic quantum mechanics. The only quantum number treated in this paper is n. This point falls far short of a finished quantum mechanics. However, even in discussion at the level of this paper, it can be concluded that quantum mechanics is an incomplete theory.

Application and Popularization of Energy Formula

In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.

Determination of Photon and Elementary Particles Rest Masses Using Maxwell’s Equations and Generalized Potential Dependent Special Relativity

The nature and origin of the photon and elementary rest masses are some of the challeng-ing problems that physics face. The approaches used to solve these problems are complex and time-consuming. Specifically, the photon rest mass pays attention to theoretical physi-cists. Many experimental works show that the photon rest mass is non zero. This problem can be solved using generalized potential dependent special relativity, which has been de-rived using simple arguments, and Maxwell’s equations, besides the conventional Einstein energy-momentum relation. The results obtained show that the rest mass of photons and elementary particles are strongly dependent on the vacuum energy and a universal con-stant. This result conforms with the models that predict time decaying vacuum energy as-sociated with production of smaller rest mass particles followed by larger masses. The two potential dependent mass expressions conform with the cosmological models that suggest the photon is generated first by assuming the universe consisting of total constant vacuum with decaying cosmological part and mass generating part. Using Maxwell’s equations, beside plank and De Broglie hypothesis together with special relativity energy-momentum relation the photon rest mass is estimated. It was shown that the photon rest mass is ex-tremely small compared to the electron mass.

Variation of Vacuum Energy if Scale Factor Becomes Infinitely Small, with Fixed Entropy Due to a Non Pathological Big Bang Singularity Accessible to Modified Einstein Equations

When initial radius Rinitial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinitial 0 are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy=0.3rH2/a2 for a time dependent horizon radius rH in cosmology, with for flat space conditions rH= for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~H2/G H≈a-1. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, Sentropy if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0.

Ground State Nucleon, Dark Energy and Dark Matter

The recently introduced model of the nucleon as a system of three point particles predicts all characteristics of the proton and neutron with experimental precision only at condition that nucleon is the loosely bound state in system of deep potential wells. The model’s Hamiltonian contains ground state with the same parity and spin as the nucleon but with other different characteristics. Existence of this ground state nucleon means that the visible Universe is composed of excited matter. The direct transition between excited and ground states is strictly forbidden, however, stimulated emission can ignite such process. Most likely, corresponding conditions realize at supernova explosion. It is shown that presence of this matter, composed of ground state nucleons, in Universe gives the chance for consistent explanation of dark matter and dark energy phenomena.

The Energy Budget of a Southwest Vortex With Heavy Rainfall over South China

Energy budgets were analyzed to study the development of an eastward propagating southwest vortex (SWV) associated with heavy rainfall over southern China(11-13 June 2008).The results show that kinetic energy(KE) generation and advection were the most important KE sources,while friction and sub-grid processes were the main KE sinks.There was downward conversion from divergent to rotational wind KE consistent with the downward stretching of SWVs.The Coriolis force was important for the formation and maintenance of the SWV.Convergence was also an important factor for maintenance,as was vertical motion during the mature stage of the SWV and the formation stage of a newly formed vortex(vortex B).The conversion from available potential energy(APE) to KE of divergent wind can lead to strong convection.Vertical motion influenced APE by dynamical and thermal processes which had opposite effects. The variation of APE was related to the heavy rainfall and convection;in this case,vertical motion with direct thermal circulation was the most important way in which APE was released,while latent heat release and vertical temperature advection were important for APE generation.