Search Results (26)

We consider a scalar QED (quantum electrodynamics) model for the frictional force and the momentum fluctuations of a polarizable particle in thermal equilibrium with radiation or in hyperbolic motion in a vacuum. In the former case the loss of particle kinetic energy due to the frictional force is compensated by the increase in kinetic energy associated with the momentum diffusion, resulting in the Planck distribution when it is assumed that the average kinetic energy satisfies the equipartition theorem. For hyperbolic motion in vacuum the frictional force and the momentum diffusion are similarly consistent with an equilibrium with a Planckian distribution at the temperature $T=\hslash a/2\pi k_{B}c$. The quantum fluctuations of the momentum imply that it is only the average acceleration a that is constant when the particle is subject to a constant applied force. Full article

This paper aimed to experimentally clarify the dynamic crushing performance of expanded polyethylene (EPE) and analyze the influence of thickness and dropping height on its mechanical behavior based on the stress–energy method. Hence, a series of impact tests are carried out on EPE foams with different thicknesses and dropping heights. The maximum acceleration, static stress, dynamic stress and dynamic energy of EPE specimens are obtained through a dynamic impact test. Then, according to the principle of the stress–energy method, the functional relationship between dynamic stress and dynamic energy is obtained through exponential fitting and polynomial fitting, and the cushion material constants a, b and c are determined. The maximum acceleration-static stress curves of any thickness and dropping height can be further fitted. By the equipartition energy domain method, the range of static stress can be expanded, which is very fast and convenient. When analyzing the influence of thickness and dropping height on the dynamic cushioning performance curves of EPE, it is found that at the same drop height, with the increase of thickness, the opening of the curve gradually becomes larger. The minimum point on the maximum acceleration-static stress curve also decreases with the increase of the thickness. When the dropping height is 400 mm, compared to foam with a thickness of 60 mm, the tested maximum acceleration value of the lowest point of the specimen with a thickness of 40 mm increased by 45.3%, and the static stress is both 5.5 kPa. When the thickness of the specimen is 50 mm, compared to the dropping height of 300 mm, the tested maximum acceleration value of the lowest point of the specimen with a dropping height of 600 mm increased by 93.3%. Therefore, the dynamic cushioning performance curve of EPE foams can be quickly obtained by the stress–energy method when the precision requirement is not high, which provides a theoretical basis for the design of cushion packaging. Full article

In classical physics, there is a well-known theorem in which it is established that the energy per degree of freedom is the same. However, in quantum mechanics, due to the non-commutativity of some pairs of observables and the possibility of having non-Markovian dynamics, the energy is not equally distributed. We propose a correspondence between what is known as the classical energy equipartition theorem and its counterpart in the phase-space formulation in quantum mechanics based on the Wigner representation. Further, we show that in the high-temperature regime, the classical result is recovered. Full article

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan–Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a “metastable” state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi–Pasta–Ulam–Tsingou (FPUT) models. We treat both the $\alpha$-FPUT and $\beta$-FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure—the spectral entropy ($\eta$)—and show that this measure has the power to quantify the distance from equipartition. For the $\alpha$-FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state $t_m$ in the $\alpha$-FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the $P_1$-$Q_1$ plane. Applying this procedure gives us a power-law scaling for $t_m$, with the important result that the power laws for different system sizes collapse down to the same exponent as $E{\alpha }^2\to 0$. We examine the energy spectrum $E\left(k\right)$ over time in the $\alpha$-FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the “wave turbulence” theory. We next apply a similar approach to the $\beta$-FPUT model. Here, we explore in particular the different behavior for the two different signs of $\beta$. Finally, we describe a procedure for calculating $t_m$ in the $\beta$-FPUT model, a very different task than for the $\alpha$-FPUT model, because the $\beta$-FPUT model is not a truncation of an integrable nonlinear model. Full article

We analyze neutrino emission channels in energetic ($\gtrsim {10}^{52}$ erg) long gamma-ray bursts within the binary-driven hypernova model. The binary-driven hypernova progenitor is a binary system composed of a carbon-oxygen star and a neutron star (NS) companion. The gravitational collapse leads to a type Ic supernova (SN) explosion and triggers an accretion process onto the NS. For orbital periods of a few minutes, the NS reaches the critical mass and forms a black hole (BH). Two physical situations produce MeV neutrinos. First, during the accretion, the NS surface emits neutrino–antineutrino pairs by thermal production. We calculate the properties of such a neutrino emission, including flavor evolution. Second, if the angular momentum of the SN ejecta is high enough, an accretion disk might form around the BH. The disk’s high density and temperature are ideal for MeV-neutrino production. We estimate the flavor evolution of electron and non-electron neutrinos and find that neutrino oscillation inside the disk leads to flavor equipartition. This effect reduces (compared to assuming frozen flavor content) the energy deposition rate of neutrino–antineutrino annihilation into electron–positron ($e^{+}{e}^{-}$) pairs in the BH vicinity. We then analyze the production of GeV-TeV neutrinos around the newborn black hole. The magnetic field surrounding the BH interacts with the BH gravitomagnetic field producing an electric field that leads to spontaneous $e^{+}{e}^{-}$ pairs by vacuum breakdown. The $e^{+}{e}^{-}$ plasma self-accelerates due to its internal pressure and engulfs protons during the expansion. The hadronic interaction of the protons in the expanding plasma with the ambient protons leads to neutrino emission via the decay chain of $\pi$-meson and $\mu$-lepton, around and far from the black hole, along different directions. These neutrinos have energies in the GeV-TeV regime, and we calculate their spectrum and luminosity. We also outline the detection probability by some current and future neutrino detectors. Full article

A universal upper limit on the entropy contained in a localized quantum system of a given size and total energy is expressed by the so-called Bekenstein bound. In a previous paper [Buoninfante, L. et al. 2022], on the basis of general thermodynamic arguments, and in regimes where the equipartition theorem still holds, the Bekenstein bound has been proved practically equivalent to the Heisenberg uncertainty relation. The smooth transition between the Bekenstein bound and the holographic bound suggests a new pair of canonical non-commutative variables, which could be thought to hold in strong gravity regimes. Full article

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts. Full article

Series solutions are used to explore the mode conversion of slow, Alfvén and fast magnetohydrodynamic waves injected at the base of a two-isothermal-layer stratified atmosphere with a uniform magnetic field, crudely representing the solar chromosphere and corona with intervening discontinuous transition region. This sets a baseline for understanding the ubiquitous Alfvénic waves observed in the corona, which are implicated in coronal heating and solar wind acceleration. It is found that all three injected wave types can partially transmit as coronal Alfvén waves in varying proportions dependent on frequency, magnetic field inclination, wave orientation, and distance between the Alfvén/acoustic equipartition level and the transition region. However, net Alfvénic transmission is limited for plausible parameters, and additional magnetic field structuring may be required to provide sufficient wave energy flux. Full article

Solar wind turbulence dominated by large-amplitude Alfvénic fluctuations, mainly propagating away from the Sun, is ubiquitous in high-speed solar wind streams. Recent observations performed in the inner heliosphere (from 1 AU down to tens of solar radii) have proved that also slow wind streams show sometimes strong Alfvénic signatures. Within this context, the present paper focuses on a comparative study on the characterization of Alfvénic turbulence in fast and slow solar wind intervals observed at 1 AU where degradation of Alfvénic correlations is expected. In particular, we compared the behavior of different parameters to characterize the Alfvénic content of the fluctuations, using also the Elsässer variables to derive the spectral behavior of the normalized cross-helicity and residual energy. This study confirms that the Alfvénic slow wind stream resembles, in many respects, a fast wind stream. The velocity-magnetic field (v-b) correlation coefficient is similar in the two cases as well as the amplitude of the fluctuations although it is not clear to what extent the condition of incompressibility holds. Moreover, the spectral analysis shows that fast wind and Alfvénic slow wind have similar normalized cross-helicity values but in general the fast wind streams are closer to energy equipartition. Despite the overall similarities between the two solar wind regimes, each stream shows also peculiar features, that could be linked to the intrinsic evolution history that each of them has experienced and that should be taken into account to investigate how and why Alfvénicity evolves in the inner heliosphere. Full article

It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures $T_i$ (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows. Full article

Granulated chelates are innovative fertilizers that are highly effective and versatile, and they ensure the best start-up effect for plants. The final properties of granules are influenced by the method of their preparation and the used substances. The diameters of the obtained granules, their size range, and the final costs of the produced fertilizer are of great importance. The paper describes granules that were produced using an agglomeration of ZnIDHA in a fluidized bed with the aid of an aqueous solution of this substance with a high dry matter content. The aim of the study was to evaluate the effect of surfactant addition to the solution on the evolution of granule size distribution during the process carried out in a batch mode and to access the possibility of describing the process dynamics using population balance approach. A sieve analysis was performed in order to determine the size of the granulate, and numerical calculations were performed to determine the value of the constant aggregation rate. Based on experimental studies, it can be seen that the increase in the diameters of granules is mainly caused by the agglomeration process, and to a lesser extent by the coating process. The addition of surfactant increased the median size of the granules in the initial granulation stage, and also lowered the surface tension. This in turn enables a lower spraying pressure to be used. A comparison of different aggregation kernels constituting an integral part of the population balance model proved that the physically motivated equipartition kinetic energy kernel performs best in this case. Moreover, the computational results show an increase in the aggregation rate when the surfactant additive is used and confirm that population balance allows the extraction of physical information about the granulation. Full article

According to Landauer’s principle, at least $k_{B}ln2T$ Joules are needed to erase a bit that stores information in a thermodynamic system at temperature T. However, the arguments for the principle rely on a regime where the equipartition principle holds. This paper, by exploring a simple model of a thermodynamic system using algorithmic information theory, shows the energy cost of transferring a bit, or restoring the original state, is $k_{B}ln2T$ Joules for a reversible system. The principle is a direct consequence of the statistics required to allocate energy between stored energy states and thermal states, and applies outside the validity of the equipartition principle. As the thermodynamic entropy of a system coincides with the algorithmic entropy of a typical state specifying the momentum degrees of freedom, it can quantify the thermodynamic requirements in terms of bit flows to maintain a system distant from the equilibrium set of states. The approach offers a simple conceptual understanding of entropy, while avoiding problems with the statistical mechanic’s approach to the second law of thermodynamics. Furthermore, the classical articulation of the principle can be used to derive the low temperature heat capacities, and is consistent with the quantum version of the principle. Full article

The process of heat exchange between two fluids of different temperatures and separated by a solid wall occurs in many engineering applications. Log mean temperature difference and effectiveness-NTU methods are widely used to assist in the design of heat exchangers. However, the two methods focus on overall analysis and cannot show the local temperature distributions. This paper obtains the mathematical solutions to the temperature profiles in an ideal counterflow heat exchanger. The aim of this research is to explain the phenomenon called the “entropy generation paradox”, which indicates a discrepancy between effectiveness and optimal entropy generation. The theoretical analysis reveals that the temperature curves are exponential functions when the heat capacity rates of the two streams are different; otherwise, the curves are linear functions. A heat exchanger is demonstrated to draw the temperature profiles under different working conditions. Local entropy generation rates are determined by the ratio of local stream temperatures in the form of a hook function. To realize a certain heat duty, there are many stream flow rate couples, and each couple results in a different entropy generation profile and obtains a corresponding total entropy generation. The helical steam generator of a high-temperature gas-cooled reactor is analyzed in this article and the principle of equipartition of entropy generation is confirmed. This principle indicates that, among the many working conditions to achieve a certain heat duty, a heat exchanger characterized by a nearly constant entropy production gives the best second law efficiency possible in order to achieve the best energy conversion. Full article

In this work, we investigate the properties of a stochastic model, in which two coupled degrees of freedom are subordinated to viscous, elastic, and also additive random forces. Our model, which builds on previous progress in Brownian motion theory, is designed to describe water-immersed microparticles connected to a cantilever nanowire prepared by polymerization using two-photon direct laser writing (TPP-DLW). The model focuses on insights into nanowires exhibiting viscoelastic behavior, which defines the specific conditions of the microbead. The nanowire bending is described by a three-parameter linear model. The theoretical model is studied from the point of view of the power spectrum density of Brownian fluctuations. Our approach also focuses on the potential energy equipartition, which determines random forcing parametrization. Analytical calculations are provided that result in a double-Lorentzian power density spectrum with two corner frequencies. The proposed model explained our preliminary experimental findings as a result of the use of regression analysis. Furthermore, an a posteriori form of regression efficiency evaluation was designed and applied to three typical spectral regions. The agreement of respective moments obtained by integration of regressed dependences as well as by summing experimental data was confirmed. Full article

The 2015 Outburst of V404 Cygni is an unusual one with several X-ray and radio flares and rapid variation in the spectral and timing properties. The outburst occurred after 26 years of inactivity of the black hole. We study the accretion flow properties of the source during its initial phase of the outburst using Swift/XRT and Swift/BAT data in the energy range of 0.5–150 keV. We have done spectral analysis with the two component advective flow (TCAF) model fits file. Several flow parameters such as two types of accretion rates (Keplerian disk and sub-Keplerian halo), shock parameters (location and compression ratio) are extracted to understand the accretion flow dynamics. We calculated equipartition magnetic field $B_{eq}$ for the outburst and found that the highest $B_{eq}\sim 900$ Gauss. Power density spectra (PDS) showed no break, which indicates no or very less contribution of the Keplerian disk component, which is also seen from the result of the spectral analysis. No signature of prominent quasi-periodic oscillations (QPOs) is observed in the PDS. This is due to the non-satisfaction of the condition for the resonance shock oscillation as we observed mismatch between the cooling timescale and infall timescale of the post-shock matter. Full article