Narrow Results

We discuss the nature of phase transitions in self-gravitating systems. We show the connection between the binary star model of Padmanabhan, the thermodynamics of stellar systems and the thermodynamics of self-gravitating fermions. We stress the inequivalence of statistical ensembles for systems with long-range interactions, like gravity. In particular, we contrast the microcanonical evolution of stellar systems from the canonical evolution of self-gravitating Brownian particles. At low energies, self-gravitating Hamiltonian systems experience a gravothermal catastrophe in the microcanonical ensemble. At low temperatures, self-gravitating Brownian systems experience an isothermal collapse in the canonical ensemble. For classical particles, the gravothermal catastrophe leads to a binary star surrounded by a hot halo while the isothermal collapse leads to a Dirac peak containing all the mass. For self-gravitating fermions, the collapse stops when quantum degeneracy comes into play through the Pauli exclusion principle. The end-product of the collapse is a fermion ball, resembling a cold white dwarf star, surrounded by a halo. We can thus describe a phase transition from a gaseous phase to a condensed phase. At high energies or high temperatures, the condensate can experience an explosion, reverse to the collapse, and return to the gaseous phase. Due to the existence of long-lived metastable states, the points of collapse and explosion differ. This leads to a notion of hysteretic cycle in microcanonical and canonical ensembles.

Correlating Shannon's maximum informational entropy variational principle with the constant value of Onicescu's informational energy, the uncertainty relations for canonical systems with SL(2R) invariance are obtained.

The constant value of Onicescu's informational energy corresponds, through transitivity manifolds of the SL(2R) group, to the ergodic theorem and, in particular case of a linear oscillator, to a quantification condition. Specifying de Broglie's idea by a periodic field in a complex coordinate, it is proved that the oscillator synchronization group of the same ensemble is still an achievement of the SL(2R) (Barbilian's group). Integrally invoking the invariant functions through the simultaneous action of the two isomorphic SL(2R) groups, the uncertainty relations and Stoler group of synchronization among oscillators from different ensembles (i.e., the second quantification when the annihilation and creation operators refer to a linear oscillator) are obtained. Barbilian's group parameters are interpreted by means of a variational principle as field amplitudes of a stationary vacuum metric.

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number $S_t$, Sisko fluid parameter $\beta$ and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and $S_t$ while their positions relocate towards the fluid–air interface with increasing $\beta$ and n. Thickness of uniform film decreases when the values of C and $S_t$ are increased whilst it increases with the increase of $\beta$ and n. Analogy between the Newtonian fluid and the Sisko fluid’s shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made.

A theoretical scheme for an experimental implementation involving bisolitonic matter waves from an attractive Bose–Einstein condensate, is considered within the framework of a non-perturbative approach to the associate Gross–Pitaevskii equation. The model consists of a single condensate subjected to an expulsive harmonic potential creating a double-condensate structure, and a gravitational potential that induces atomic exchanges between the two overlapping post condensates. Using a non-isospectral scattering transform method, exact expressions for the bright-matter–wave bisolitons are found in terms of double-lump envelopes with the co-propagating pulses displaying more or less pronounced differences in their widths and tails depending on the mass of atoms composing the condensate.

The dynamics of a two-soliton molecule bouncing on the reflecting atomic mirror under the effect of gravity have been studied by analytical and numerical methods. The analytical description is based on the variational approximation. In numerical simulations, we observe the resonance oscillations of the two-soliton’s center-of-mass position and width, induced by modulated atomic mirror. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation (GPE) and qualitative agreement between them is found. Hamiltonian dynamic system for a dipolar Bose–Einstein condensates (BECs) has been studied.

The quest for a microscopic foundation of thermodynamics is addressed within the Nonunitary Newtonian Gravity (NNG) model through the study of a specific closed system, namely, a three-dimensional harmonic nanocrystal. A numerical calculation of the nanocrystal von Neumann entropy as a function of time is performed, showing a sharp monotonic increase, followed by a stabilization at late times. This behavior is consistent with the emergence of a microcanonical ensemble within the initial energy levels, signaling, in this way, the establishment of a nonunitary gravity-induced thermal equilibrium.

The model of generalized thermoelasticity, with the dual-phase-lag theory (DPL), is applied to study the influence of gravity on a piezo-thermoelastic diffusive medium. Normal mode analysis is used to obtain the exact expressions for different physical quantities. The derived expressions are computed numerically and the results are presented in graphical form. Comparisons are made with the results predicted by the Lord–Shulman theory (LS) and the DPL model in the presence and absence of gravity.

In this paper, a novel model in a nonlocal porous thermoelastic solid is formulated based on the dual-phase-lag model (DPL), the Lord–Shulman theory and coupled theory with a memory-dependent derivative. The Laplace–Fourier technique is used to solve the problem and to obtain the exact expressions of physical fields. Numerical calculation of temperature, displacement, change in the volume fraction and stress is carried out and displayed graphically. Comparisons are made with the results predicted in the absence and presence of the gravity field as well as a nonlocal parameter. Comparisons are also made with results for different memory Kernel.