Isotropic Fluid Research Articles

Partial Differential Equations with Quadratic Nonlinearities Viewed as Matrix-Valued Optimal Ballistic Transport Problems

We study a rather general class of optimal “ballistic” transport problems for matrix-valued measures. These problems naturally arise, in the spirit of Brenier (Commun Math Phys 364(2):579–605, 2018), from a certain dual formulation of nonlinear evolutionary equations with a particular quadratic structure reminiscent both of the incompressible Euler equation and of the quadratic Hamilton–Jacobi equation. The examples include the ideal incompressible MHD, the template matching equation, the multidimensional Camassa–Holm (also known as the $$H({{\,\mathrm{div}\,}})$$ geodesic equation), EPDiff, Euler- $$\alpha $$ , KdV and Zakharov–Kuznetsov equations, the equations of motion for the incompressible isotropic elastic fluid and for the damping-free Maxwell’s fluid. We prove the existence of the solutions to the optimal “ballistic” transport problems. For formally conservative problems, such as the above mentioned examples, a solution to the dual problem determines a “time-noisy” version of the solution to the original problem, and the latter one may be retrieved by time-averaging. This yields the existence of a new type of absolutely continuous in time generalized solutions to the initial-value problems for the above mentioned PDE. We also establish a sharp upper bound on the optimal value of the dual problem, and explore the weak–strong uniqueness issue.

Role of energy–momentum squared gravity on the dynamics of charged dissipative plane symmetric collapse

This paper deals with the dynamics of charged plane symmetric collapse with dissipative fluid distribution in the framework of energy–momentum squared gravity. For this purpose, we consider non-static plane symmetric spacetime in the inner and static charged Vaidya spacetime in the outer regions of a star. We use Darmois junction conditions to match the interior and exterior geometries and find that masses of both spacetimes are identical if and only if their correspondence charges are same. To investigate the dynamics of the system, we apply Misner–Sharp and Müler–Israel–Stewart approaches to formulate dynamical as well as transport equations, respectively. We then couple these equations to analyze the effect of physical quantities and modified terms on the collapse rate. A relation among Weyl tensor, electromagnetic field and fluid variables, is also developed. Due to the influence of charge, anisotropic pressure and modified terms, the spacetime is not conformally flat. Further, we assume isotropic fluid and ignore the impact of electromagnetic field which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the presence of a charge, effective pressure, heat flux and additional terms of this gravity.

Nonlocal extension of causal thermodynamics of the isotropic cosmic fluid

We establish the nonlocal generalization of the Israel-Stewart model for the relativistic causal thermodynamics of the cosmic fluid, which evolves in the homogeneous isotropic Universe. Based on the second law of thermodynamics we derive the integro-differential master equation for the nonequilibrium pressure scalar and reduce it to the differential equation of the second order in time derivatives. We show that this master equation can be considered as the relativistic analog of the Burgers equation, which is known in the classical theory of viscoelasticity. We obtain the nonlinear key equation, which contains the energy density scalar only, and analyze two exact solutions of the model. The effective temperature is considered to be associated with the barotropic equation of state of the cosmic fluid.

Electrically Powered Locomotion of Dual-Nature Colloid-Hedgehog and Colloid-Umbilic Topological and Elastic Dipoles in Liquid Crystals.

Colloidal particles in liquid crystals tend to induce topological defects and distortions of the molecular alignment within the surrounding anisotropic host medium, which results in elasticity-mediated interactions not accessible to their counterparts within isotropic fluid hosts. Such particle-induced coronae of perturbed nematic order are highly responsive to external electric fields, even when the uniformly aligned host medium away from particles exhibits no response to fields below the realignment threshold. Here we harness the nonreciprocal nature of these facile electric responses to demonstrate colloidal locomotion. Oscillations of the electric field prompt repetitive deformations of the corona of dipolar elastic distortions around the colloidal inclusions, which upon appropriately designed electric driving synchronize the displacement directions. We observe the colloid-hedgehog dipole accompanied by an umbilical defect in the tilt directionality field (c-field), along with the texture of elastic distortions that evolves with a change in the applied voltage. The temporal out-of-equilibrium evolution of the director and c-field distortions around particles when the voltage is turned on and off is not invariant upon reversal of time, prompting lateral translations and interactions that markedly differ from those accessible to these colloids under equilibrium conditions. Our findings may lead to both technological and fundamental science applications of nematic colloids as both model reconfigurable colloidal systems and as mesostructured materials with predesigned temporal evolution of structure and composition.

Recent analytic development of the dynamic $ Q $-tensor theory for nematic liquid crystals

<abstract><p>Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and $ Q $-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the $ Q $-tensor theory in dynamic configurations.</p></abstract>

Segmenting White Matter Hyperintensities on Isotropic Three-Dimensional Fluid Attenuated Inversion Recovery Magnetic Resonance Images: A Comparison of Deep Learning Tools on a Norwegian National Imaging Database

Segmenting White Matter Hyperintensities on Isotropic Three-Dimensional Fluid Attenuated Inversion Recovery Magnetic Resonance Images: A Comparison of Deep Learning Tools on a Norwegian National Imaging Database

A simple predictor of interface orientation of fluids of disk-like anisotropic particles and its implications for organic semiconductors.

From classical molecular dynamics simulations, we identify a simple and general predictor of molecular orientation at solid and vapour interfaces of isotropic fluids of disk-like anisotropic particles based on their shape and interaction anisotropy. For a wide variety of inter-particle interactions, temperatures, and substrate types within the range of typical organic semiconductors and their processing conditions, we find remarkable universal scaling of the orientation at the interface with the free energy calculated from pair interactions between close-packed nearest neighbours and an empirically derived universal relationship between the entropy and the shape anisotropy and bulk volume fraction of the fluid particles. The face-on orientation of fluid particles at the solid interface is generally predicted to be the equilibrium structure, although the alignment can be controlled by tuning the particle shape and substrate type, while changing the strength of fluid-fluid interactions is likely to play a less effective role. At the vapour interface, only the side-on structure is predicted, and conditions for which the face-on structure may be preferred, such as low temperature, low interaction anisotropy, or low shape anisotropy, are likely to result in little orientation preference (due to the low anisotropy) or be associated with a phase transition to an anisotropic bulk phase for systems with interactions in the range of typical organic semiconductors. Based on these results, we propose a set of guidelines for the rational design and processing of organic semiconductors to achieve a target orientation at a solid or vapour interface.

Assembling Microtubule-Based Active Matter.

Studied for more than a century, equilibrium liquid crystals provided insight into the properties of ordered materials, and led to commonplace applications such as display technology. Active nematics are a new class of liquid crystal materials that are driven out of equilibrium by continuous motion of the constituent anisotropic units. A versatile experimental realization of active nematic liquid crystals is based on rod-like cytoskeletal filaments that are driven out of equilibrium by molecular motors. We describe protocols for assembling microtubule-kinesin based active nematic liquid crystals and associated isotropic fluids. We describe the purification of each protein and the assembly process of a two-dimensional active nematic on a water-oil interface. Finally, we show examples of nematic formation and describe methods for quantifying their non-equilibrium dynamics.

Hydrodynamic theory of flocking at a solid-liquid interface: Long-range order and giant number fluctuations.

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a passive, isotropic bulk fluid and a solid surface are dynamically coupled to the bulk fluid. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations," i.e., large fluctuations of the number of active particles in a fixed large area. Specifically, these number fluctuations grow as the 3/4th power of the mean number within the area. Stable systems also exhibit anomalously rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is nonanomalous. In other parameter regimes, the system becomes unstable.

Role of f(G) gravity in the study of non-static complex systems

The concept of complexity for dynamical spherically symmetric dissipative self-gravitating configuration (Herrera et al. Phys. Rev. D, 98, 104059 (2018). doi:10.1103/PhysRevD.98.104059) is generalized in the scenario of modified Gauss–Bonnet gravity. For this purpose, a spherically symmetric fluid with locally anisotropic, dissipative, and non-dissipative configurations is considered. We choose the same complexity factor for the structure as we did for the static case, while we consider the homologous condition for the simplest pattern of evolution. In this approach, we formulate structure scalars that demonstrate the essential properties of the system. A fluid distribution that fulfills the vanishing complexity constraint and proceeds homologously corresponds to isotropic, geodesic, homogeneous, and shear-free fluid. In the dissipative case, the fluid is still geodesic but it is shearing, and there is a wide range of solutions. In the last, the stability of vanishing complexity is examined.

Dynamic soil consolidation model using a nonlocal continuum poroelastic damage approach

AbstractWe present a novel dynamic poroelastic model for soil consolidation in an isotropic homogeneous fluid saturated porous media. A nonlocal integral‐type continuum damage formulation is applied to describe the damage evolution under dynamic excitations, in which a bilinear damage law is assumed. The governing equations are obtained by considering the conservation of momentum and mass balance for the solid–fluid mixtures, in which the fluid flow obeys Darcy's seepage law in the entire domain. The numerical solution of the fully coupled problem is achieved via a mixed FEM displacement–pressure element formulation. The mechanical equilibrium equations are evolved in time using a Newmark method and the resulting nonlinear system is solved via a Newton–Raphson method. Consistent linearization is then used to obtain the block Jacobian matrix analytically and the linear system is solved monolithically at each time step. Several numerical results are presented to study soil consolidation problems under harmonic excitations. We investigate the time‐dependence response of the skeleton displacement, pressure, and damage evolution. In addition, the examples demonstrate that the nonlocal integral‐type damage model can effectively overcome mesh dependence and yield smooth behavior.

Dark energy stars in Tolman–Kuchowicz spacetime in the context of Einstein gravity

Dark energy is the component in the present Universe with the greatest abundance, and it is responsible for the accelerating expansion of the Universe. As a result, dark energy is likely to interact with any compact astrophysical object [Muhammad F.A.R. Sakti and Anto Sulaksono, {\it Phys. Rev. D} {\bf 103}, 084042 (2021)]. In present paper, we propose a model for a dark energy star made up of dark and ordinary matter in which the density of dark energy is proportional to the density of isotropic perfect fluid matter. In the context of general relativity, the model is derived in the curved Tolman-Kuchowicz spacetime geometry [Tolman, Phys Rev 55:364, (1939); Kuchowicz, Acta Phys Pol 33:541, (1968)]. Here, we look at how dark energy affects stellar mass, compactness, and equilibrium etc. The physical parameters of the model e.g., pressure, density, mass function, surface redshift etc. are investigated, and the stability of stellar configuration is studied in detail. The model has interesting properties because it meets all energy criteria and is free from central singularities. The maximum allowable mass has been obtained from our model with the help of $M-R$ diagram. We analyse many physical properties of the model and checked that it meets all regularity constraints, is stable, and therefore physically realistic.

Study of stellar structures in f(ℛ,𝒯μν𝒯μν) theory

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of [Formula: see text] gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine the impacts of correction terms and effective fluid parameters on the dynamics of a cylindrical star. A correlation between the Weyl tensor and physical quantities is also developed. The conformally flat condition is not obtained due to the influence of anisotropic pressure and higher-order nonlinear terms. Further, we assume isotropic fluid and specific model of this theory which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the inclusion of effective pressure and additional terms of this theory.

Viscometry of Electron Fluids from Symmetry.

When electrons flow as a viscous fluid in anisotropic metals, the reduced symmetry can lead to exotic viscosity tensors with many additional, nonstandard components. We present a viscometry technique that can, in principle, measure the multiple dissipative viscosities allowed in isotropic and anisotropic fluids alike. By applying representation theory to exploit the intrinsic symmetry of the fluid, our viscometry is also exceptionally robust to both boundary complications and ballistic effects. We present the technique via the illustrative example of dihedral symmetry, relevant in this context as the point symmetry of 2D crystals. Finally, we propose a present-day realizable experiment for detecting, in a metal, a novel hydrodynamic phenomenon: the presence of rotational dissipation in an otherwise isotropic fluid.

Modeling, measurements and validation of magnetic field dependent flow behavior of magnetorheological fluids; static and dynamic yield stress

The issue which is always debated in the magnetorheological (MR) fluid is the dynamic and static yield stress values obtained from a flow curve. To evaluate these, a suitable constitutive equations are required. The aim of this article is to provide suitable rheological models for the prediction of static and dynamic yield stress from a single flow curve under wide shear rate and magnetic field ranges. The proposed model is well suited for isotropic and anisotropic particle-based MR fluids. The parameters, like yield stress, critical shear rate and viscosity at high shear rate obtained from the fit show systematic variation with applied magnetic field strength. These variations in the parameters can be related to the mesostructure formation and its influence on the MR suspension rheological properties. To further confirm the value of the static yield stress derived from the proposed model, the small-strain oscillatory shear flow experiment is carried out and the static yield stress values are obtained. These values agree well with that obtained from the proposed model. Similarly, to evaluate the dynamic yield stress from the flow curve, modified three parameter model applied to soft glassy materials is used. Here, the critical shear rate parameter obtained from the proposed model is used to deduce dynamic yield stress. It is identified that the values obtained are lower than the static yield stress. Furthermore, at low magnetic field, the static and dynamic yield stress follows the relationship defined by the square dependence of the magnetic field strength. The difference between the static and dynamic yield stress values at high field is greater for anisotropic particle based MR fluid than isotropic particle based MR fluid. This reflects the contribution of particle-particle and particle-carrier interaction in the value of the yield stress in anisotropic particle based MR fluid. Thus, the present model provides a clear idea of the dissipation process that occurs in a shear MR fluid.

Effect of Photonic Band Gap on Photoluminescence in a Dye-Doped Blue Phase Liquid Crystal.

Tunability of fluorescence intensity is an essential parameter for enhancing the versatility of devices like emissive displays and solar cells. Soft photonic crystals, with their tunable photonic band gap (PBG), are highly sought-after systems for such purposes. Here, we report modulation of photoluminescence (PL) intensity in a fluorescent dye-doped blue phase liquid crystal, a 3D soft photonic crystal. On cooling, from the isotropic fluid phase, the PL intensity gets enhanced due to the overlapping of the emission wavelength of the dye with the photonic band edge. However, the PL intensity decreases on the application of an electric field, despite both thermal and electric fields having a similar effect (red shift) on the PBG. The contrasting behavior of PL intensity, also observed in composites obtained by varying the dye and the chiral dopant (handedness), is discussed in terms of scattering pathways for the emitted photons. The time-resolved PL studies show a reduction in the lifetime of the excited species upon cooling, validating the thermal dependence of PL intensity modulation due to Purcell effect. The facile modulation of PL intensity in the dye-doped blue phase system makes it appealing from the point of view of high-performance photonic applications.

Charged anisotropic fluid sphere in comparison with its uncharged analogue through extended geometric deformation

In this article, we consider a known charged isotropic Durgapal IV solution and extend it to its anisotropic version using gravitational decoupling by means of extended geometric deformation (EGD) approach, which provides a more generic way for the decoupling of gravitational sources. Following this approach, we employ linear transformation on both metric potentials and split the original set of field equations into two subsystems. The first subsystem corresponds to charged isotropic fluid while the second one is related to the additional source, crucial for anisotropy. The isotropic one is specified through metric functions of known charged isotropic solution, while the solution of second sector is determined by considering two different constraints on additional source Θab, i.e., mimicking of isotropic pressure and a linear equation of state which relating Θ00 and Θ11. The matching conditions at the stellar surface are discussed in detail, where outer geometry is represented by Reissner–Nordstrom solution. We discuss the physical properties of the stellar model in comparison with its uncharged anisotropic analogue, which is provided in Appendix. Physical analysis is carried out using different physical indicators including energy conditions, equilibrium equation, casualty condition, Herrera’s cracking concept, adiabatic index, compactness and surface redshift for compact star PSR J 1416-2230. We find that anisotropic stellar model is stable for larger range of γ (coupling constant) in the presence of electric charge and the effects of anisotropy are diminished near stellar surface.

Homogeneous perfect fluid collapse in five-dimensional spherically symmetric spacetime

In this paper, the higher-dimensional collapse of homogeneous isotropic perfect fluid is studied by considering the geometry of five-dimensional spherically symmetric metric. Using equations of state for different fields like dust, radiation and stiff fluid with and without cosmological constant [Formula: see text], the gravitational collapse is studied. The results are compared with the usual four-dimensional study in [A. V. Astashenok, K. Mosani, S. D. Odintsov and G. C. Samanta, Int. J. Geom. Methods Mod. Phys. 16, 1950035 (2019)]. It is found that the collapse rate is faster in five-dimensional spacetime as compared to four-dimensional case supporting the cosmic censorship hypothesis.

Mass correction and deformation of slowly rotating anisotropic neutron stars based on Hartle\u2013Thorne formalism

Due to their compactness, neutron stars are the best study matter in high density and strong-field gravity. Hartle and Thorne have proposed a good approximation or perturbation procedure within general relativity for slowly rotating relativistic stars by assuming the matter inside the stars is an ideal isotropic fluid. This study extends the analytical Hartle–Thorne formalism for slowly rotating neutron stars, including the possibility that the neutron star pressure can be anisotropic. We study the impact of neutron stars’ anisotropy pressure on mass correction and deformation numerically. For the anisotropic model, we use the Bowers-Liang model. For the equation of state of neutron stars, we use a relativistic mean-field BSP parameter set with the hyperons, and for the crust equation of state, we use the one of Miyatsu et al. We have found that the mass of neutron stars increases but the radius decreases by increasing lambda _{BL} value. Therefore, the NS compactness increases when lambda _{BL} becomes larger. This fact leads to a condition in which NS is getting harder to deformed when the lambda _{BL} increased.

General isotropic micropolar fluid model in smoothed particle hydrodynamics.

The smoothed particle hydrodynamics (SPH) method is used in this paper to model micropolar fluids, with emphasis on their dissipation mechanisms. To this aim, a dissipation function is defined at the particle level which depends on the relative velocity between particles but also on an additional spin degree of freedom, which modifies such relative velocity as well as introduces spin-related intrinsic dissipation mechanisms, comparable to those related to the rate of deformation tensor in Newtonian fluids. This dissipation function is then incorporated within the Lagrangian formalism, leading to a set of SPH particle equations to describe the dynamics. A continuous integral SPH version of the scheme is obtained with a bottom-up derivation which guarantees the consistency of the SPH term. The model is then enriched with two additional terms based exclusively on the spin derivatives, which grant it the maximal generality as an isotropic model for micropolar fluids. Finally, numerical verification and validation tests are documented that show that SPH is capable of accurately modeling this type of dynamics.