Classical Kinetic Energy Research Articles

The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth

Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions, the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant second-, third-, fourth-, and fifth-order nonlinear terms though a suitable canonical transformation. The four kernels of the equation and the 18 coefficients of the transformation are expressed in explicit form in terms of the expansion coefficients of the gravity wave Hamiltonian in integral-power series in normal variables. The possibilities of the existence of integrals of motion for the wave momentum and the wave action are discussed, particularly the special integrals for the latter. For ocean surface capillary–gravity waves on a fluid with a finite depth, the sixth-order expansion coefficients of the Hamiltonian in integral-power series in normal variables are concretely provided, thus naturally including the classical fifth-order kinetic energy expansion coefficients given by Krasitskii.

Toward local Madelung mechanics in spacetime

It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in spacetime. For want of a fully relativistic quantum fluid treatment, we develop a model using the nonrelativistic Madelung equations, and obtain conditions for them to be local in spacetime. Every particle in the Madelung fluid is equally real, and has a definite position, momentum, kinetic energy, and potential energy. These are obtained by defining quantum momentum and kinetic energy densities for the fluid and separating the momentum into average and symmetric parts, and kinetic energy into classical kinetic and quantum potential parts. The two types of momentum naturally give rise to a single classical kinetic energy density, which contains the expected kinetic energy, even for stationary states, and we define the reduced quantum potential as the remaining part of the quantum kinetic energy density. We treat the quantum potential as a novel mode of internal energy storage within the fluid particles, which explains most of the nonclassical behavior of the Madelung fluid. For example, we show that in tunneling phenomena, the quantum potential negates the barrier so that nothing prevents the fluid from flowing through. We show how energy flows and transforms in this model, and that enabling local conservation of energy requires defining a quantum potential energy current that flows through the fluid rather than only flowing with it. The nonrelativistic treatment generally contains singularities in the velocity field, which undermines the goal of local dynamics, but we expect a proper relativistic treatment will bound the fluid particle velocities at c.

Homogenization of Dissipative Hamiltonian Systems Under Lévy Fluctuations

We study the small mass limit for a class of Hamiltonian systems with multiplicative non-Gaussian Lévy noise. Derivation of the limiting equation depends on the structure of the stochastic Hamiltonian systems, in which a discontinuous noise-induced drift term arises. Firstly, we show that the momentum in the stochastic Hamiltonian system converges to zero when the kinetic energy has polynomial growth. Then, we prove that the stochastic Hamiltonian system with classical kinetic energy converges to the limiting equation in probability, with respect to Skorokhod topology as the mass tends to zero.

Quasienergy operators and generalized squeezed states for systems of trapped ions

Collective many-body dynamics for time-dependent quantum Hamiltonians is investigated for a dynamical system that exhibits multiple degrees of freedom, in this case a combined (Paul and Penning) trap. Quantum stability is characterized by a discrete quasienergy spectrum, while the quasienergy states are symplectic coherent states. We introduce the generators of the Lie algebra of the symplectic group SL(2,R), which we use to build the coherent states (CS) associated to the system under investigation. The trapped ion is treated as a harmonic oscillator (HO) to which we associate the quantum Hamilton function. We obtain the kinetic and potential energy operators as functions of the Lie algebra generators and supply the expressions for the classical coordinate, momentum, kinetic and potential energy, along with the total energy. Moreover, we also infer the dispersions for the coordinate and momentum, together with the asymmetry and the flatness parameter for the distribution. The system interaction with laser radiation is also examined for a system of identical two-level atoms. The Hamilton function for the Dicke model is derived. The optical system is modelled as a HO (trapped ion) that undergoes interaction with an external laser field and we use it to engineer a squeezed state of the electromagnetic (EM) field. We consider coherent and squeezed states associated to both ion dynamics and to the EM field. The approach used enables one to build CS in a compact and smart manner by use of the group theory.

Modeling and free vibration analysis for bolted composite plate under inconsistent pre-tightening condition

During the service process of bolted composite structures, the local bolt pre-tightening force may decrease, that is, the bolts are inconsistently pre-tightening, which will affect the integrity of the whole system. Here, a semi-analytical modeling method for bolted composite plates with inconsistent pre-tightening conditions is studied. To simulate the uneven pressure distribution on the bolted joint surface, a variable stiffness spring surface model is proposed and a method to obtain the parameters of the model is also described. For a specific connection structure, each joint is simplified into a spring surface model and modeling of inconsistent bolt preload in the connection structure could be realized by assigning different parameters to each spring surface model. Based on the classical laminate plate theory, the strain and kinetic energy of the composite plate are calculated and the motion equation of the structures is deduced by the Rayleigh-Ritz method. Finally, a modal test is applied for a multi-bolted fiber-reinforced composite plate. The accuracy of the model is verified by both test and 3D finite element analysis results. The influence of loosening degree, position and quantity of loosening bolts on natural frequencies of bolted composite plates is further analyzed.

Interaction of vector Bose gases with fermionic superfluids

We study the effects of vector Bose gases, which are described by massive vector Bose fields, on fermionic superfluids in the low-energy region. It is demonstrated that the vector Bose gases can give rise to the Meissner effect, the flux quantization, and the Josephson effect, which are similar to those of the electromagnetic field in fermionic superfluids. However, unlike the electromagnetic field where the Meissner effect is unrelated to mass and the quantized flux is a constant, the Meissner effect of the vector Bose gases can be related to mass via a classical kinetic energy, and the value of the quantized flux is tunable. Our analyses also show that, although the origin model violates gauge invariance, the vector Bose gases in fact are gauge-invariant Maxwell-Chern-Simons systems under a Gauss constraint. It is also proposed that these effects can be observed by using the spin-1 cold atomic Bose gases in experiments.

Study on Application of New Kinetic Energy Theorem of Rigid Body Fixed-Axis Rotation

The classical kinetic energy theorem of rigid body fixed-axis rotation cannot correctly reflect non-conservative force doing dissipative work, non-conservative reacting force doing equivalent dissipative work at the same time, instead convert the system’s mechanical energy into the non-mechanical energy of the bearer. Now these defects are overcome by the new kinetic energy theorem of rigid body fixed-axis rotation.The meaning of new kinetic energy theorem of rigid body fixed-axis rotation is interpreted, the procedures to solve practical problems on new kinetic energy theorem of rigid body fixed-axis rotation and computing methods of the terms in the new kinetic energy theorem of rigid body fixed-axis rotation are studied, as well as the physical significance of the results is described.

Steep eternal inflation and the swampland

I investigate whether eternal inflation is possible when the inflaton originally travels upslope the scalar potential and inevitably reaches a turn-around point where its classical kinetic energy momentarily vanishes. This behaviour occurs regardless of the steepness of the potential slope. Such steep eternal inflation, if achieved, would satisfy the recent swampland conjecture and allow eternal inflation in the string landscape.

A molecular dynamics study of nuclear quantum effect on diffusivity of hydrogen molecule.

In this paper, the nuclear quantum effect of the hydrogen molecule on its diffusivity was analyzed using the molecular dynamics (MD) method. The centroid MD (CMD) method was applied to reproduce the time evolution of the molecules. The diffusion coefficient of hydrogen was calculated using the Green-Kubo method over a wide temperature region, and the temperature dependence of the quantum effect of the hydrogen molecule on its diffusivity was addressed. The calculated results were compared with classical MD results based on the principle of corresponding state (PCS). It was confirmed that the difference in the diffusion coefficient calculated in the CMD and classical MD methods was small, and the PCS appears to be satisfied on the temperature dependence of the diffusion coefficient, even though the quantum effect of the hydrogen molecules was taken into account. It was clarified that this result did not suggest that the quantum effect on the diffusivity of the hydrogen molecule was small but that the two changes in the intermolecular interaction of hydrogen due to the quantum effect offset each other. Moreover, it was found that this tendency was related to the temperature dependence of the ratio of the kinetic energy of the quantum fluctuational motion to the classical kinetic energy.

A Diagnosis of Excessive Mixing in Smagorinsky Subfilter-Scale Turbulent Kinetic Energy Models

Abstract Large-eddy simulation (LES) models are widely used to study atmospheric turbulence. The effects of small-scale motions that cannot be resolved need to be modeled by a subfilter-scale (SFS) model. The SFS contribution to the turbulent fluxes is typically significant in the surface layer. This study presents analytical solutions of the classical Smagorinsky SFS turbulent kinetic energy (TKE) model including a buoyancy flux contribution. Both a constant length scale and a stability-dependent one as proposed by Deardorff are considered. Analytical expressions for the mixing functions are derived and Monin–Obukhov similarity relations that are implicitly imposed by the SFS TKE model are diagnosed. For neutral and weakly stable conditions, observations indicate that the turbulent Prandtl number (PrT) is close to unity. However, based on observations in the convective boundary layer, a lower value for PrT is often applied in LES models. As a lower Prandtl number promotes a stronger mixing of heat, this may cause excessive mixing, which is quantified from a direct comparison of the mixing function as imposed by the SFS TKE model with empirical fits from field observations. For a strong stability, the diagnosed mixing functions for both momentum and heat are larger than observed. The problem of excessive mixing will be enhanced for anisotropic grids. The findings are also relevant for high-resolution numerical weather prediction models that use a Smagorinsky-type TKE closure.

Theory of Stochastic Schrödinger Equation in Complex Vector Space

A generalized Schrodinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrodinger equation may be called stochastic Schrodinger equation. It is found that the second order correction terms are similar to corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrodinger equation reduces to normal Schrodinger equation. It is found that the Schrodinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrodinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein–Gordon equation is derived by squaring the stochastic Schrodinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations.

Chaotic distributions for relativistic particles

We study a modified Kac model where the classical kinetic energy is replacedby an arbitrary energy function $\phi(v)$, $v \in \mathbb{R}$. The aim of this paperis to show that the uniform density with respect to the microcanonicalmeasure is $Ce^{-z_0\phi(v)}$-chaotic, $C,z_0 \in \mathbb{R}_+$. The kinetic energyfor relativistic particles is a special case. A generalization to the case$v\in \mathbb{R}^d$ which involves conservation momentum is also formally discussed.

On a Fractal Version of Witten’s M-Theory

Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

Generalized stochastic flows and applications to incompressible viscous fluids

We introduce a notion of generalized stochastic flows on manifolds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends the classical kinetic energy to Brownian flows, defined as the L2 norm of their drift. We prove that there exists a generalized flow which realizes the infimum of the kinetic energy among all generalized flows with prescribed initial and final configuration. We also construct generalized flows with prescribed drift and kinetic energy smaller than the L2 norm of the drift.The results are actually presented for general Lq norms, thus including not only the Navier–Stokes equations but also other equations such as the porous media.

Quantum physics of an elementary system in de Sitter space

We present the coherent states of a scalar massive particle on 1+3-de Sitter space. These states are vectors in Hilbert space, and they are labeled by points in the associated phase space. To do this, we use the fact that the phase space of a scalar massive particle on 1+3-de Sitter space is a cotangent bundle “T∗(S3)” which is isomorphic with the complex sphere “\(S_{\mathbb{C}}^{3}\)”. Then by using the heat kernel on “\(S_{\mathbb{C}}^{3}\)” that was presented by Hall–Mitchell, we construct our coherent states. At the end, by these states we quantize the classical kinetic energy on de Sitter space.

Cryogenic Helium Adsorbed in Zeolite Rho: Inside Localization Controlled Self-Diffusion of Confined Quantum Particles

Applying Feynman’s treatment of quantum mechanics at finite temperatures via path integrals and the numerical analytic continuation method developed recently (Kowalczyk, P.; Gauden, P. A.; Terzyk, A. P.; Furmaniak, Sylwester, J. Chem. Theory Comput.2009, 5, 1990–1996), we study the mobility of 4He atoms adsorbed in zeolite rho at 40 K. At studied temperature, the self-diffusive motion of 4He atoms in zeolite rho is strongly concentration-dependent. At low pore concentrations, 4He atoms are adsorbed in high-energetic adsorption centers of the zeolite. Due to strong localization in the solid–fluid potential well, an average kinetic energy of 4He atoms at infinite dilution reaches ∼120 K (i.e., twice of the classical kinetic energy at 40 K, Eclass = 60 K), whereas the self-diffusion constant drops up to ∼0.001 Å2 ps–1. Increasing pore concentration of 4He leads to the rapid increase in mobility of adsorbed 4He atoms. We show that ∼8 mmol cm–3, self-diffusive motion of confined 4He atoms increases up to ∼1 Å2 ps–1. Variation of the kinetic energy, potential energy, and enthalpy of 4He adsorption with pore concentration indicates that high-energetic adsorption sites in studied zeolite sample are saturated at low pore densities. The remaining adsorption sites are characterized by weaker solid–fluid potential, which allows higher delocalization of adsorbed 4He atoms. The reported novel phenomenon of localization controlled self-diffusion of confined 4He seems to be promising for smart designing of nanoporous quantum molecular sieves and storage nanovessels. Understanding of 4He cryogenic adsorption in the smallest pores enriches our knowledge that is crucial for precise analysis of ultramicropore sizes.

Numerical simulation and decomposition of kinetic energy in the Central Mediterranean: insight on mesoscale circulation and energy conversion

Abstract. The spatial and temporal variability of eddy and mean kinetic energy of the Central Mediterranean region has been investigated, from January 2008 to December 2010, by mean of a numerical simulation mainly to quantify the mesoscale dynamics and their relationships with physical forcing. In order to understand the energy redistribution processes, the baroclinic energy conversion has been analysed, suggesting hypotheses about the drivers of the mesoscale activity in this area. The ocean model used is based on the Princeton Ocean Model implemented at 1/32° horizontal resolution. Surface momentum and buoyancy fluxes are interactively computed by mean of standard bulk formulae using predicted model Sea Surface Temperature and atmospheric variables provided by the European Centre for Medium Range Weather Forecast operational analyses. At its lateral boundaries the model is one-way nested within the Mediterranean Forecasting System operational products. The model domain has been subdivided in four sub-regions: Sardinia channel and southern Tyrrhenian Sea, Sicily channel, eastern Tunisian shelf and Libyan Sea. Temporal evolution of eddy and mean kinetic energy has been analysed, on each of the four sub-regions, showing different behaviours. On annual scales and within the first 5 m depth, the eddy kinetic energy represents approximately the 60 % of the total kinetic energy over the whole domain, confirming the strong mesoscale nature of the surface current flows in this area. The analyses show that the model well reproduces the path and the temporal behaviour of the main known sub-basin circulation features. New mesoscale structures have been also identified, from numerical results and direct observations, for the first time as the Pantelleria Vortex and the Medina Gyre. The classical kinetic energy decomposition (eddy and mean) allowed to depict and to quantify the permanent and fluctuating parts of the circulation in the region, and to differentiate the four sub-regions as function of relative and absolute strength of the mesoscale activity. Furthermore the Baroclinic Energy Conversion term shows that in the Sardinia Channel the mesoscale activity, due to baroclinic instabilities, is significantly larger than in the other sub-regions, while a negative sign of the energy conversion, meaning a transfer of energy from the Eddy Kinetic Energy to the Eddy Available Potential Energy, has been recorded only for the surface layers of the Sicily Channel during summer.

Quantum molecular dynamics simulation formultifragmentation resulting from an expandingnuclear matter

Quantum molecular dynamics (QMD) is used to investigate multifragmentation resulting from an expanding nuclear matter. Equation of state, the structure of nuclear matter and symmetric nu-clear matter is discussed. Also, the dependence of the fragment mass distribution on the initial temperature (Tinit) and the radial flow velocity (h) is studied. When h is large, the distribution shows exponential shape, whereas for small h, it obeys the exponentially falling distribution with mass number. The cluster formation in an expanding system is found to be different from the one in a thermally equilibrated system. The used Hamiltonian has a classical kinetic energy term and an effective potential term composed of four parts.

Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson’s stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N−1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. We then write the N-electron classical kinetic energy as the sum of the (one-electron) classical kinetic energy and another (N−1)-electron kinetic correlation term. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase, and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases. Finally, we underline that, although our aim in this paper is conceptual rather than practical, our results are potentially useful for the construction of improved kinetic-energy functionals.

Variational approach to dequantization

We present a dequantization procedure based on a variational approach whereby quantum fluctuations latent in the quantum momentum are suppressed. This is done by adding generic local deformations to the quantum momentum operator which give rise to a deformed kinetic term quantifying the amount of 'fuzziness' caused by such fluctuations. Considered as a functional of such deformations, the deformed kinetic term is shown to possess a unique minimum which is seen to be the classical kinetic energy. Furthermore, we show that extremization of the associated deformed action functional introduces an essential nonlinearity to the resulting field equations which are seen to be the classical Hamilton–Jacobi and continuity equations. Thus, a variational procedure determines the particular deformation that has the effect of suppressing the quantum fluctuations, resulting in dequantization of the system.