821 research outputs found
The effects of nonlocality on the evolution of higher order fluxes in non-equilibrium thermodynamics
The role of gradient dependent constitutive spaces is investigated on the
example of Extended Thermodynamics of rigid heat conductors. Different levels
of nonlocality are developed and the different versions of extended
thermodynamics are classified. The local form of the entropy density plays a
crucial role in the investigations. The entropy inequality is solved under
suitable constitutive assumptions. Balance form of evolution equations is
obtained in special cases. Closure relations are derived on a phenomenological
level.Comment: 16 pages, 1 figur
Archimedean-type force in a cosmic dark fluid: II. Qualitative and numerical study of a multistage Universe expansion
In this (second) part of the work we present the results of numerical and
qualitative analysis, based on a new model of the Archimedean-type interaction
between dark matter and dark energy. The Archimedean-type force is linear in
the four-gradient of the dark energy pressure and plays a role of
self-regulator of the energy redistribution in a cosmic dark fluid. Because of
the Archimedean-type interaction the cosmological evolution is shown to have a
multistage character. Depending on the choice of the values of the model
guiding parameters,the Universe's expansion is shown to be perpetually
accelerated, periodic or quasiperiodic with finite number of
deceleration/acceleration epochs. We distinguished the models, which can be
definitely characterized by the inflation in the early Universe, by the
late-time accelerated expansion and nonsingular behavior in intermediate
epochs, and classified them with respect to a number of transition points.
Transition points appear, when the acceleration parameter changes the sign,
providing the natural partition of the Universe's history into epochs of
accelerated and decelerated expansion. The strategy and results of numerical
calculations are advocated by the qualitative analysis of the instantaneous
phase portraits of the dynamic system associated with the key equation for the
dark energy pressure evolution.Comment: 15 pages, 12 figures, Part II, typos corrected, Fig.4 replaced,
references correcte
Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature
By assuming a self-similar structure for Kelvin waves along vortex loops with
successive smaller scale features, we model the fractal dimension of a
superfluid vortex tangle in the zero temperature limit. Our model assumes that
at each step the total energy of the vortices is conserved, but the total
length can change. We obtain a relation between the fractal dimension and the
exponent describing how the vortex energy per unit length changes with the
length scale. This relation does not depend on the specific model, and shows
that if smaller length scales make a decreasing relative contribution to the
energy per unit length of vortex lines, the fractal dimension will be higher
than unity. Finally, for the sake of more concrete illustration, we relate the
fractal dimension of the tangle to the scaling exponents of amplitude and
wavelength of a cascade of Kelvin waves.Comment: 12 pages, 1 figur
Test of Information Theory on the Boltzmann Equation
We examine information theory using the steady-state Boltzmann equation. In a
nonequilibrium steady-state system under steady heat conduction, the
thermodynamic quantities from information theory are calculated and compared
with those from the steady-state Boltzmann equation. We have found that
information theory is inconsistent with the steady-state Boltzmann equation.Comment: 12 page
Hyperbolic subdiffusive impedance
We use the hyperbolic subdiffusion equation with fractional time derivatives
(the generalized Cattaneo equation) to study the transport process of
electrolytes in media where subdiffusion occurs. In this model the flux is
delayed in a non-zero time with respect to the concentration gradient. In
particular, we obtain the formula of electrochemical subdiffusive impedance of
a spatially limited sample in the limit of large and of small pulsation of the
electric field. The boundary condition at the external wall of the sample are
taken in the general form as a linear combination of subdiffusive flux and
concentration of the transported particles. We also discuss the influence of
the equation parameters (the subdiffusion parameter and the delay time) on the
Nyquist impedance plots.Comment: 10 pages, 5 figure
Stability of inflationary solutions driven by a changing dissipative fluid
In this paper the second Lyapunov method is used to study the stability of
the de Sitter phase of cosmic expansion when the source of the gravitational
field is a viscous fluid. Different inflationary scenarios related with
reheating and decay of mini-blackholes into radiation are investigated using an
effective fluid described by time--varying thermodynamical quantities.Comment: 17 pages, LaTeX 2.09, 2 figures. To be published in Classical and
Quantum Gravit
Steady shear flow thermodynamics based on a canonical distribution approach
A non-equilibrium steady state thermodynamics to describe shear flows is
developed using a canonical distribution approach. We construct a canonical
distribution for shear flow based on the energy in the moving frame using the
Lagrangian formalism of the classical mechanics. From this distribution we
derive the Evans-Hanley shear flow thermodynamics, which is characterized by
the first law of thermodynamics relating infinitesimal
changes in energy , entropy and shear rate with kinetic
temperature . Our central result is that the coefficient is given by
Helfand's moment for viscosity. This approach leads to thermodynamic stability
conditions for shear flow, one of which is equivalent to the positivity of the
correlation function of . We emphasize the role of the external work
required to sustain the steady shear flow in this approach, and show
theoretically that the ensemble average of its power must be
non-negative. A non-equilibrium entropy, increasing in time, is introduced, so
that the amount of heat based on this entropy is equal to the average of
. Numerical results from non-equilibrium molecular dynamics simulation
of two-dimensional many-particle systems with soft-core interactions are
presented which support our interpretation.Comment: 23 pages, 7 figure
Possible experiment to check the reality of a nonequilibrium temperature
An experiment is proposed to check the physical reality of a nonequilibrium absolute temperature previously proposed from theoretical grounds in the framework of extended irreversible thermodynamics
Magnetic relaxation in the Bianchi-I universe
Extended Einstein-Maxwell model and its application to the problem of
evolution of magnetized Bianchi-I Universe are considered. The evolution of
medium magnetization is governed by a relaxation type extended constitutive
equation. The series of exact solutions to the extended master equations is
obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is
shown to become non-monotonic (accelerated/decelerated) in both principal
directions (along the magnetic field and orthogonal to it). A specific type of
expansion, the so-called evolution with hidden magnetic field, is shown to
appear when the magnetization effectively screens the magnetic field and the
latter disappears from the equations for gravitational field.Comment: 32 page
Some analytical models of radiating collapsing spheres
We present some analytical solutions to the Einstein equations, describing
radiating collapsing spheres in the diffusion approximation. Solutions allow
for modeling physical reasonable situations. The temperature is calculated for
each solution, using a hyperbolic transport equation, which permits to exhibit
the influence of relaxational effects on the dynamics of the system.Comment: 17 pages Late
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