Internal Energy Density Research Articles

Effect of a Nanodisperse Graphite on the Viscoelastic Properties of Polyvinyl Chloride

In the absence of segregation of nanodisperse graphite particles, obtained by electrolysis as a new filler of polyvinyl chloride (PVC), the viscoelastic phenomena dependent on the structural changes of a composite are investigated. The shear modulus and the volume compressibility caused by deviations of elements of the structure from the quasi-equilibrium state under the action of ultrasonic vibrations (ω = 0.4·106 0.4 · 10 s–1) are calculated at filler concentrations 0 ≤ φ ≤ 10.0 vol.% and temperatures 298 K ≤ T ≤ (Tg + 10) K. It is shown that the volume density of internal energy depends on the expectation time for the transition of structural elements through the energy barrier, the dynamic viscosity of the material, and temperature. The results of calculations serve as the basis for producing PVC systems with controllable of properties.

PATCHWORK: A Multipatch Infrastructure for Multiphysics/Multiscale/Multiframe Fluid Simulations

We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element is a sophisticated client-router-server framework for efficiently linking processors supporting different regions ("patches") that must exchange boundary data. This infrastructure may be used with a wide variety of fluid dynamics codes; the only requirement is that their primary dependent variables be the same in all patches, e.g., fluid mass density, internal energy density, and velocity. Its structure can accommodate either Newtonian or relativistic dynamics. The overhead imposed by this system is both problem- and computer cluster architecture-dependent. Compared to a conventional simulation using the same number of cells and processors, the increase in runtime can be anywhere from negligible to a factor of a few; however, one of the infrastructure's advantages is that it can lead to a very large reduction in the total number of zone-updates.

Effect of the cosmological constant on the deflection angle by a rotating cosmic string

We report the effect of the cosmological constant and the internal energy density of a cosmic string on the deflection angle of light in the spacetime of a rotating cosmic string with internal structure. We first revisit the deflection angle by a rotating cosmic string and then provide a generalization using the geodesic equations and the Gauss-Bonnet Theorem. We show there is an agreement between the two methods when employing higher order terms of the linear mass density of the cosmic string. By modifying the integration domain for the global conical topology, we resolve the inconsistency between these two methods previously reported in the literature. We show that the deflection angle is not affected by the rotation of the cosmic string; however, the cosmological constant $\Lambda$ strongly affects the deflection angle, which generalizes the well-known result.

Dissipative Properties of EHD Lubricant Film

For the case of the failure of the lubricant film at hydrodynamic lubrication a common thermodynamic theory of strength is considered. According to this theory the failure occurs when the internal energy density (potential and thermal components) in the volume of material reaches a constant for a given material. A special case of this theory is considered when only the density of heat (kinetic) component of internal energy is taken into account. Temperature condition determines the limit state for liquid lubricants - mineral oils. When analyzing the regularities of friction at EHD lubrication the state and properties of the oil film at the condition of irregular and hydrostatic compression. The original structural model of oil film at EHD lubrication in the form of the rotary oscillating cells with elastic interactions to each other is proposed. It is similar to the Rayleigh-Benard cells and corresponds to the cellular hypothesis of J. Gibbs for the case of equilibrium and reversible process. It is quite possible that the size of the cells have an order of about nano level. The oil film dissipates energy in the direction of relative motion of bodies. This oil film has the highest dissipative properties.

Numerical investigation of kinetic turbulence in relativistic pair plasmas – I. Turbulence statistics

We describe results from particle-in-cell simulations of driven turbulence in collisionless, magnetized, relativistic pair plasma. This physical regime provides a simple setting for investigating the basic properties of kinetic turbulence and is relevant for high-energy astrophysical systems such as pulsar wind nebulae and astrophysical jets. In this paper, we investigate the statistics of turbulent fluctuations in simulations on lattices of up to $1024^3$ cells and containing up to $2 \times 10^{11}$ particles. Due to the absence of a cooling mechanism in our simulations, turbulent energy dissipation reduces the magnetization parameter to order unity within a few dynamical times, causing turbulent motions to become sub-relativistic. In the developed stage, our results agree with predictions from magnetohydrodynamic turbulence phenomenology at inertial-range scales, including a power-law magnetic energy spectrum with index near $-5/3$, scale-dependent anisotropy of fluctuations described by critical balance, log-normal distributions for particle density and internal energy density (related by a $4/3$ adiabatic index, as predicted for an ultra-relativistic ideal gas), and the presence of intermittency. We also present possible signatures of a kinetic cascade by measuring power-law spectra for the magnetic, electric, and density fluctuations at sub-Larmor scales.

The contribution of a directional preference of stiffness to the efficacy of prophylactic sacral dressings in protecting healthy and diabetic tissues from pressure injury: computational modelling studies.

The sacral region is the most common site for pressure injuries (PIs) associated with lying in bed, and such sacral PIs often commence as deep tissue injuries (DTIs) that later present as open wounds. In complex patients, diabetes is common. Because, among other factors, diabetes affects connective tissue stiffness properties, making these tissues less able to dissipate mechanical loads through physiological deformations, diabetes is an additional biomechanical risk factor for PIs and DTIs. A preventive measure with established successful clinical outcomes is the use of sacral prophylactic dressings. The objective of this study has been to expand our previous work regarding the modes of action and biomechanical efficacy of prophylactic dressings in protecting the soft tissues adjacent to the sacrum by specifically examining the role of a directional stiffness preference (anisotropy) of the dressing while further accounting for diabetic tissue conditions. Multiple three-dimensional anatomically detailed finite element (FE) model variants representing diabetic tissue conditions were used, and tissue loading state data were compared with healthy tissue simulations. We specifically compared soft tissue exposures to elevated internal shear stresses and strain energy densities (SED) near the sacrum during supine weight bearing on a standard (foam) hospital mattress without a dressing, with a prophylactic dressing lacking directional stiffness preferences and with an anisotropic dressing. Our results have clearly shown that an anisotropic dressing design reduces the peak tissue stresses and exposure to sustained tissue deformations in both healthy and diabetic cases. The present study provides additional important insights regarding the optimal structural and material design of prophylactic dressings, which in turn, informs clinicians and decision makers regarding beneficial features.

On magnetohydrodynamic gauge field theory

Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963 Can. J. Phys. 41 2241–51). It is shown how the polarization vector in Calkin’s approach naturally arises from the Lagrange multiplier constraint equation for Faraday’s equation for the magnetic induction , or alternatively from the magnetic vector potential form of Faraday’s equation. Gauss’s equation, (divergence of is zero) is incorporated in the variational principle by means of a Lagrange multiplier constraint. Noether’s theorem coupled with the gauge symmetries is used to derive the conservation laws for (a) magnetic helicity, (b) cross helicity, (c) fluid helicity for non-magnetized fluids, and (d) a class of conservation laws associated with curl and divergence equations which applies to Faraday’s equation and Gauss’s equation. The magnetic helicity conservation law is due to a gauge symmetry in MHD and not due to a fluid relabelling symmetry. The analysis is carried out for the general case of a non-barotropic gas in which the gas pressure and internal energy density depend on both the entropy S and the gas density ρ. The cross helicity and fluid helicity conservation laws in the non-barotropic case are nonlocal conservation laws that reduce to local conservation laws for the case of a barotropic gas. The connections between gauge symmetries, Clebsch potentials and Casimirs are developed. It is shown that the gauge symmetry functionals in the work of Henyey (1982 Phys. Rev. A 26 480–3) satisfy the Casimir determining equations.

Free-energy functional of the Debye–Hückel model of two-component plasmas

We present a generalization of the Debye–Hückel free-energy-density functional of simple fluids to the case of two-component systems with arbitrary interaction potentials. It allows one to obtain the two-component Debye–Hückel integral equations through its minimization with respect to the pair correlation functions, leads to the correct form of the internal energy density, and fulfills the virial theorem. It is based on our previous idea, proposed for the one-component Debye–Hückel approach, which was published recently in Ref. [1]. We use the Debye–Kirkwood charging method in the same way as in Ref. [1], in order to build an expression of the free-energy density functional. Main properties of the two-component Debye–Hückel free energy are presented and discussed, including the virial theorem in the case of long-range interaction potentials.

Unified low-parametrical equation used to calculate the viscosity coefficient of argon

Using the previously obtained dependence of excess viscosity on internal energy density and low-parametric unified equation of state for calculation of thermodynamic properties of liquid, gas, and fluid, the equation for the excess viscosity of argon in the range of the “mixed” mechanism of momentum transfer in the shear flow was derived. Different versions of approximation of excess viscosity dependence on the density of interaction energy were compared, and the optimal version of this dependence was determined. A simple unified low-parametric equation was obtained for describing the coefficient of argon viscosity in a wide range of state parameters. It is shown that the proposed low-parametric equation for calculating the viscosity coefficient of liquid and gas allows reliable extrapolation beyond the studied region.

Thermal fluctuations of pair interaction forces in liquid Yukawa systems

The dynamics of charged particles in two- and three-dimensional Yukawa systems is studied using numerical methods. Nonideal systems are simulated in a wide range of their parameters. The density of thermal fluctuations of pair interaction forces in liquid structures is obtained and compared with the internal energy density of the systems under study.

The Internal Pressure and Cohesive Energy Density of Liquid Metallic Elements

The internal pressures, \(P_{\mathrm{int}}\), of practically all the liquid metallic elements in the periodic table up to plutonium (except highly radioactive ones) at their melting points were calculated from data in the literature. They are compared with the respective cohesive energy densities, ced, obtained from the literature data too. The ratios \(P_{\mathrm{int}}{/}ced\) for various liquids are ranked as follows: molten salts < polar/hydrogen-bonded molecular solvents \(\sim \) liquid metals < room temperature ionic liquids < nonpolar molecular solvents, and the reverse of this list reflects the relative strengths of the mutual interactions of the particles constituting these liquids.

Planck scale effects on the thermodynamics of photon gases

A particular framework for quantum gravity is the doubly special relativity (DSR) formalism that introduces a new observer independent scale (the Planck scale). We resort to the methods of statistical mechanics in this framework to determine how the deformed dispersion relation affects the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, free energy and specific heat are calculated. These results are compared with the outcome obtained in the Lorentz violating model of Camacho and Marcias (Gen. Relativ. Gravit. 39: 1175-1183, 2007). The two types of models predict different results due to different spacetime structure near the Planck scale. The resulting modifications can be interpreted as a consequence of the deformed Lorentz symmetry present in the particular model we have considered. In the low energy limit, our calculation coincides with usual results of photon thermodynamics in special relativity (SR) theory, in contrast to the study presented in (Phys. Rev. D81, 085039 (2010)).

Thermal effects of a photon gas with a deformed Heisenberg algebra

In this paper, we have considered the thermodynamics of a photon gas subject to the presence of a minimal measurable length following from a covariant extension of the original generalized uncertainty principle (GUP). After consistently establishing a generalized dynamics, we define a GUP deformed Maxwell invariant which serves as the basis for our study. In order to highlight the GUP effects, we compute the one- and two-loop order contribution to the partition function at the high-temperature limit. Afterwards, by computing the internal energy density, we conclude that the additional terms can be seen as corrections [Formula: see text] to the Stefan–Boltzmann law due to GUP effects.

THE INTERNAL STRUCTURE OF OVERPRESSURED, MAGNETIZED, RELATIVISTIC JETS

ABSTRACT This work presents the first characterization of the internal structure of overpressured, steady superfast-magnetosonic relativistic jets in connection with their dominant type of energy. To this aim, relativistic magnetohydrodynamic simulations of different jet models threaded by a helical magnetic field have been analyzed covering a wide region in the magnetosonic Mach number–specific internal energy plane. The merit of this plane is that models dominated by different types of energy (internal energy: hot jets; rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux-dominated jets) occupy well-separated regions. The analyzed models also cover a wide range of magnetizations. Models dominated by the internal energy (i.e., hot models, or Poynting-flux-dominated jets with magnetizations larger than but close to one) have a rich internal structure characterized by a series of recollimation shocks and present the largest variations in the flow Lorentz factor (and internal energy density). Conversely, in kinetically dominated models, there is not much internal or magnetic energy to be converted into kinetic, and the jets are featureless with small variations in the flow Lorentz factor. The presence of a significant toroidal magnetic field threading the jet produces large gradients in the transversal profile of the internal energy density. Poynting-flux-dominated models with high magnetization (≈10 or larger) are prone to be unstable against magnetic pinch modes, which sets limits on the expected magnetization in parsec-scale active galactic nucleus jets or constrains their magnetic field configuration.

Global embeddings and hydrodynamic properties of Kerr black hole

In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies, we study the black holes GRO J1655-40 and 4U 1543-47 to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of 1.0 ly around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9 + 3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane, we investigate the warp products of the Kerr spacetime.

Thermal fluctuations of the pair-interaction forces in two-dimensional fluid Yukawa systems

In the paper, the particle dynamics in two-dimensional (2D) Yukawa systems were studied numerically. New data on a density of the thermal fluctuations of pair-interaction forces have been obtained for non-ideal systems in a wide range of their parameters. Comparisons of these thermal fluctuations with the internal energy density were performed. For the first time we have found, that for strongly correlated fluid 2D Yukawa systems the dielectric constant is inversely proportional to the second derivative of a pair potential at the mean inter-particle distance.

Parameterized neutron star and proto-neutron star equation of state at finite temperature

Read et al. proposed a parameterized equation of state (EOS) giving the pressure \(P\) as a function of the rest mass density \(\rho\) in a piecewise polytropic form for the study of neutron stars. The parameterized piecewise polytropic EOS can accurately represent many realistic EOS tables at zero temperature. We showed that the treatment can be extended to finite temperature to cover the study of neutron star at non zero temperature and proto-neutron stars. At finite temperature, two types of thermodynamic relations are needed, one for the pressure \(P\) and one for the internal energy density \(u\). We show that for many finite temperature realistic EOS tables, both the \(P\) and \(u\) can be accurately represented in piecewise polytropic forms as functions of the rest mass density \(\rho\) and temperature \(T\). The polytropic parameterization provides a framework to compare and understand the properties of the different realistic EOSs.

Thermal radiative and thermodynamic properties of solid and liquid uranium and plutonium carbides in the visible–near-infrared range

The knowledge of thermal radiative and thermodynamic properties of uranium and plutonium carbides under extreme conditions is essential for designing a new metallic fuel materials for next generation of a nuclear reactor. The present work is devoted to the study of the thermal radiative and thermodynamic properties of liquid and solid uranium and plutonium carbides at their melting/freezing temperatures. The Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and normal total emissivity are calculated using experimental data for the frequency dependence of the normal spectral emissivity of liquid and solid uranium and plutonium carbides in the visible-near infrared range. It is shown that the thermal radiative and thermodynamic functions of uranium carbide have a slight difference during liquid-to-solid transition. Unlike UC, such a difference between these functions have not been established for plutonium carbide. The calculated values for the normal total emissivity of uranium and plutonium carbides at their melting temperatures is in good agreement with experimental data. The obtained results allow to calculate the thermal radiative and thermodynamic properties of liquid and solid uranium and plutonium carbides for any size of samples. Based on the model of Hagen-Rubens and the Wiedemann-Franz law, a new method to determine the thermal conductivity of metals and carbides at the melting points is proposed.

The internal pressure and cohesive energy density of two inorganic liquids: Bromine and carbon disulfide

The internal pressures, Pint, of two inorganic liquids: bromine and carbon disulfide were calculated from data in the literature and compared with their cohesive energy densities, ced. The values are in the ranges obtained for common organic liquids, but the ratio of ced/Pint for bromine is larger than might be expected for this non-polar but polarizable substance.

An irreversible port-Hamiltonian formulation of distributed diffusion processes

Abstract: An infinite dimensional formulation of IPHS is proposed for a general class of mass and heat diffusion processes. The structure of the system is derived from the expression of the internal entropy creation, and just as for the lumped case the IPHS structure is expressed as a function of the distributed thermodynamic driving forces and a positive definite function containing the thermodynamic parameters of the different diffusion processes. The distributed thermodynamic driving forces are expressed as the evaluation of the internal energy density and entropy density on a pseudo-Poisson bracket defined by the skew-adjoint differential operator defining the coupling between the different energy domains. This is analogous to the case of lumped IPHS, where the pseudo-Poisson bracket is defined not by differential operators but by constant (canonical) skew-symmetric matrices.