Irrotational Research Articles

(m,ρ)-quasi-Einstein solitons on 3-dimensional trans-Sasakian manifolds and its applications in spacetimes

This paper characterizes [Formula: see text]-quasi-Einstein solitons on [Formula: see text]-dimensional trans-Sasakian manifolds. It has been shown that a closed [Formula: see text]-quasi-Einstein soliton on a [Formula: see text]-dimensional trans-Sasakian manifold is either cosymplectic or Einstein under certain restrictions. Moreover, we investigate [Formula: see text]-quasi-Einstein solitons with certain potential vector fields on [Formula: see text]-dimensional trans-Sasakian manifolds. As an application of this soliton, we also analyze super quasi-Einstein spacetimes whose metrics are associated with [Formula: see text]-quasi-Einstein solitons.

η-Ricci–Yamabe Solitons along Riemannian Submersions

In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the η-Ricci–Yamabe soliton (η-RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an η-RY soliton, an η-Ricci soliton, and an η-Yamabe soliton. Additionally, we consider the many circumstances under which a target manifold of Riemannian submersion is an η-RY soliton, an η-Ricci soliton, an η-Yamabe soliton, or a quasi-Yamabe soliton. We deduce a Poisson equation on a Riemannian submersion in a specific scenario if the potential vector field ω of the soliton is of gradient type =:grad(γ) and provide some examples of an η-RY soliton, which illustrates our finding. Finally, we explore a number theoretic approach to Riemannian submersion with totally geodesic fibers.

Transonic Flow Computation Over A Heat Shield Using Three Dimensional Finite Element Method

A three dimensional finite element method is employed for solution of the transonic full potential equation in mass conservation form. The finite element analysis allows the boundary conditions to be treated in simple and exact manner, without the use of a mapping scheme. The full potential equation is based on the assumption of irrotational flow and density of the fluid is calculated using isentropic relation and it is applicable for upstream local Mach number upto 1.6. The nonlinear full potential equation is reduced to a set of nonlinear algebraic equation using Galerkin’s formulation. An iterative scheme in conjunction with the artificial viscosity term is used to solve the set of algebraic equations. The artificial viscosity term stabilizes the numerical scheme and captures the shock very well. An appropriate grid arrangement is selected in the algorithm to maintain proper and continuous linkage between upstream and downstream of the flow at the centroid of the hexahedral element. The surface pressure distribution in the freestream Mach number range 0.80 - 0.95 and at an angle of incidence 5 degree shows a fairly good agreement with the experimental data. The present finite element discretization can be coupled with the commercially available software.

Results of Hyperbolic Ricci Solitons

We obtain some properties of a hyperbolic Ricci soliton with certain types of potential vector fields, and we point out some conditions when it reduces to a trivial Ricci soliton. We also study those soliton submanifolds whose vector fields are the tangential components of a concurrent vector field on the ambient manifold, and in particular, we show that a totally umbilical hyperbolic Ricci soliton is an Einstein manifold. We prove that if the hyperbolic Ricci soliton hypersurface of a Riemannian manifold of constant curvature and endowed with a concurrent vector field has a parallel shape operator, then it is a metallic-shaped hypersurface, and we determine some conditions for it to be minimal. Moreover, we show that it is also a pseudosymmetric hypersurface.

Turbulent/non-turbulent interfaces in equilibrium and non-equilibrium regions in the absence of mean shear

Direct numerical simulations (DNS) of turbulent fronts evolving into a non-turbulent flow region in the absence of mean shear are generated for both classical (equilibrium) and non-equilibrium turbulence in order to study the characteristics of the turbulent/non-turbulent interface (TNTI) that separates regions of turbulent from non-turbulent (or irrotational) flow. The effects of the non-equilibrium can be observed in a number of statistics computed in the turbulent core region of the turbulent evolving fronts, such as the Reynolds dependance of the normalised dissipation Cɛ, which exhibits a power law (for non-equilibrium turbulence) close to Cɛ∼Reλ−n, where Reλ is the Taylor based Reynolds number and n≈1 is a constant. However the non-equilibrium condition of the turbulent core region does not affect the main characteristics of the TNTI layer bounding this region, which is similar in equilibrium and non-equilibrium turbulence. In particular, the thickness of the TNTI layer is similar in both equilibrium and non-equilibrium turbulence.

Existence of Finite Global Norm of Potential Vector Field in a Ricci Soliton

Existence of Finite Global Norm of Potential Vector Field in a Ricci Soliton

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity ρL=1/2 on the smallest scale (r = 0) is a unique feature of collisionless flow (ρL=1 for incompressible flow). On large scale, transverse velocity correlation has an exponential form T2∝e−r/r2 with a constant comoving scale r2=21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of S2l∝r1/4. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

On 1 + 3 covariant perturbations of the quasi-Newtonian spacetime in modified Gauss–Bonnet gravity

The consideration of a [Formula: see text] covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of [Formula: see text] gravity theory in this study. This approach reveals the existence of integrability conditions which do not appear in noncovariant treatments. We constructed the integrability conditions in modified Gauss–Bonnet [Formula: see text] gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in [Formula: see text] gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian spacetime were constructed in the context of modified [Formula: see text] gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behavior of the overdensity and velocity perturbations using [Formula: see text] model was made. On the other hand, we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short- and long-wavelength modes in a dust-Gauss–Bonnet fluids was done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to [Formula: see text]CDM, it means [Formula: see text] the considered [Formula: see text] model results coincide with [Formula: see text]CDM.

Asymptotic behaviors for the Jordan–Moore–Gibson–Thompson equation in the viscous case

In this paper, we study large-time behaviors for a fundamental model in nonlinear acoustics, precisely, the viscous Jordan–Moore–Gibson–Thompson (JMGT) equation in the whole space Rn. This model describes nonlinear acoustics in perfect gases under irrotational flow and equipping Cattaneo’s law of heat conduction. By employing refined WKB analysis and Fourier analysis, we derive first- and second-order asymptotic profiles of solution to the Moore–Gibson–Thompson (MGT) equation as t≫1, which illustrates novel optimal estimates for the solutions even subtracting its profiles. Concerning the nonlinear JMGT equation, via suggesting a new decomposition of nonlinear portion, we investigate the existence and large-time profiles of global (in time) small data Sobolev solutions with suitable regularity. These results help bridge a new connection between the JMGT equation and diffusion-waves as t≫1.

Characterizations of perfect fluid spacetimes obeying f(ℛ)-gravity equipped with different gradient solitons

The prime object of this paper is to study the perfect fluid spacetimes obeying [Formula: see text]-gravity, when [Formula: see text]-Ricci solitons, gradient [Formula: see text]-Ricci solitons, gradient Einstein solitons and gradient [Formula: see text]-quasi Einstein solitons are its metrics. At first, the existence of the [Formula: see text]-Ricci solitons is proved by a non-trivial example. We establish conditions for which the [Formula: see text]-Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying [Formula: see text]-gravity, when the potential vector field of [Formula: see text]-Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient [Formula: see text]-Ricci solitons, gradient Einstein solitons and gradient [Formula: see text]-quasi Einstein solitons in [Formula: see text]-gravity, respectively. As a result, we establish some significant theorems about dark matter era.

Geometry of almost contact metrics as an almost ∗-η-Ricci–Bourguignon solitons

In this paper, we give some characterizations by considering almost ∗-[Formula: see text]-Ricci–Bourguignon soliton as a Kenmotsu metric. It is shown that if a Kenmotsu metric endows a ∗-[Formula: see text]-Ricci–Bourguignon soliton, then the curvature tensor R with the soliton vector field V is given by the expression [Formula: see text] Next, we show that if an almost Kenmotsu manifold such that [Formula: see text] belongs to [Formula: see text]-nullity distribution where [Formula: see text] acknowledges a ∗-[Formula: see text]-Ricci–Bourguignon soliton satisfying [Formula: see text], then the manifold is Ricci-flat and is locally isometric to [Formula: see text]. Moreover if the metric admits a gradient almost ∗-[Formula: see text]-Ricci–Bourguignon soliton and [Formula: see text] leaves the scalar curvature r invariant on a Kenmotsu manifold, then the manifold is an [Formula: see text]-Einstein. Also, if a Kenmotsu metric represents an almost ∗-[Formula: see text]-Ricci–Bourguignon soliton with potential vector field V is pointwise collinear with [Formula: see text], then the manifold is an [Formula: see text]-Einstein.

A new fluid-structure coupling model: Case of a pipe under internal pressure

This work presents the eigenfrequencies of a study on the fluid-structure interaction for a pipe with a circular section, under pressure constraints in laminar, incompressible and irrotational flow, followed by a comparison between stiffness coupling and bar coupling with different geometric ratio Radius/Length; Radius/Thickness, as a frequency geometric identity of the pipe in the industry. The realization of this study is to have better coupling, where we use the relations of mechanical behaviour of the solid on displacement-stress and for the fluid, we use the Navier-Stokes equations in cylindrical coordinates under the speed-stress form transformed into displacement by the Galerkin-Temp theory. Either the force of the fluid will be distributed on the internal surface of the cylinder by the coupling (interface) between fluid and solid. To obtain the results of the eigenfrequencies we used the hierarchical finite element method (HFEM) for both mechanical and fluid entities. For the natural frequencies, we apply the hierarchical finite elements of the Legendre polynomial which is defined in a well-known interval, thanks to this mathematical calculation we arrive at the general equations of motion matrix form of the solid, the interface and the fluid. The calculation was carried out by a MATLAB programme which determines the eigenfrequencies of the evolved system by different geometric and physical parameters mentioned. We validated this work by a table of comparison between the experimental values and the values of the programme.

Nonlinear Dynamics of Perturbations of a Plane Potential Fluid Flow: Nonlocal Generalization of the Hopf Equation

In this paper, we analytically study the two-dimensional unsteady irrotational flow of an ideal incompressible fluid in a half-plane whose boundary is assumed to be a linear sink. It is shown that the nonlinear evolution of perturbations of the initial uniform flow is described by a one-dimensional integro-differential equation, which can be considered as a nonlocal generalization of the Hopf equation. This equation can be reduced to a system of ordinary differential equations (ODEs) in the cases of spatially localized or spatially periodic perturbations of the velocity field. In the first case, ODEs describe the motion of a system of interacting virtual point vortex-sinks/sources outside the flow domain. In the second case, ODEs describe the evolution of a finite number of harmonics of the velocity field distribution; this is possible due to the revealed property of the new equation that the interaction of initial harmonics does not lead to generation of new ones. The revealed reductions made it possible to effectively study the nonlinear evolution of the system, in particular, to describe the effect of nonlinearity on the relaxation of velocity field perturbations. It is shown that nonlinearity can significantly reduce the relaxation rate by more than 1.5 times.

Electromagnetic wave representation as a superposition of the quantized vector potential field of single photons

Without stating postulates or advancing any hypothesis, we show that a physical representation for the photon results directly from Maxwell’s theory once the vector potential amplitude is normalized at a single photon level. Electromagnetic waves are composed of a superposition of single photon states with circular polarizations, each extended over a wavelength and occupying a specific quantization volume. This representation is valid at any frequency and consequently can be applied for the modeling of advanced devices ranging from X-Rays and UV applications to fiber optics, microwave antennas and radio waves emitters.

A study on conformal Ricci solitons and conformal Ricci almost solitons within the framework of almost contact geometry

The goal of this paper is to find some important Einstein manifolds using conformal Ricci solitons and conformal Ricci almost solitons. We prove that a Kenmotsu metric as a conformal Ricci soliton is Einstein if it is an $\eta$-Einstein or the potential vector field $V$ is infinitesimal contact transformation or collinear with the Reeb vector field $\xi$. Next, we prove that a Kenmotsu metric as gradient conformal Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariant. Finally, we have embellished an example to illustrate the existence of conformal Ricci soliton and gradient almost conformal Ricci soliton on Kenmotsu manifold.

Stability characteristics of the cylindrical power-law viscoelastic fluid interface with heat transfer

The analytical study of heat and mass transport at the viscous fluid-viscoelastic fluid is carried out using the irrotational flow theory of viscous-viscoelastic fluids. The interface of viscous-viscoelastic fluid experiences capillary instability. The viscoelastic fluid is taken as power-law fluid and both asymmetric and axisymmetric disturbances are analyzed. The fluids are enclosed in an annular region bounded by two rigid concentric cylinders. The non-dimensional dispersion relation depends on the capillary number, Weber number, power-law index, heat transfer coefficient, viscosity ratio of fluids, etc. The transfer of heat and mass has a significant impact on the stability of the interface. It is also found that the viscosity of viscous fluid delays instability.

Geometry of almost contact metrics as a ∗-conformal Ricci–Yamabe solitons and related results

The goal of this paper is to study certain types of metric such as ∗-conformal Ricci–Yamabe soliton (RYS), whose potential vector field is torse-forming on Kenmotsu manifold. Here, we establish the conditions for solitons to be expanding, shrinking or steady and find the scalar curvature when the manifold admits ∗-conformal RYS on Kenmotsu manifold. Next, we developed the nature of the vector field when the manifold satisfies ∗-conformal RYS. Also, we have adorned some applications of torse-forming vector field in terms of ∗-conformal RYS on Kenmotsu manifold. We have also studied infinitesimal CL-transformation and Schouten–van Kampen connection on Kenmotsu manifold, whose metric is ∗-conformal RYS. We present an example of ∗-conformal RYS on three-dimensional Kenmotsu manifold, and verify some of our findings.

Varvec{J}-, M- and varvec{L}-integrals of line charges and line forces

In this work, the varvec{J}-, M- and varvec{L}-integrals of two line charges and two line forces in generalized plane strain are derived in the framework of three-dimensional (3D) electrostatics and three-dimensional compatible linear elasticity, respectively, in order to study the interaction between them. The key point in this derivation is achieved by expressing the varvec{J}-, M- and varvec{L}-integrals of point charges and point forces in three dimensions in terms of the corresponding three-dimensional Green functions, that is, the three-dimensional Green function of the Laplace operator and the three-dimensional Green tensor of the Navier operator, respectively. The major mathematical tool used in deriving the varvec{J}-, M- and L_3-integrals of line charges and line forces from the corresponding varvec{J}-, M- and varvec{L}-integrals of point charges and point forces is the method of embedding or method of descent of Green functions to two dimensions (2D) from the corresponding Green functions in 3D. The analytical expressions of varvec{J}-, M- and L_3-integrals of line charges and line forces in antiplane and plane strain are derived and discussed. The varvec{J}-integral is the electrostatic part of the Lorentz force (electrostatic interaction force) between two line charges in electrostatics and the Cherepanov force between two line forces in elasticity. The M-integral of two line sources (charges or forces) equals half the electrostatic interaction energy in electrostatics and half the elastic interaction energy in elasticity of these two line sources, respectively. The L_3-integral of two line sources (charges or forces) is the z-component of the configurational vector moment or the rotational moment representing the total torque about the z-axis caused by the interaction of the two line sources. An important outcome is that the varvec{J}-integral is twice the negative gradient of the M-integral, leading to the result that the {varvec{J}}-integral for line charges and line forces is a conservative force (with the corresponding interaction energy playing the role of the potential energy) and consequently an irrotational vector field. Finally, the obtained varvec{J}-, M- and L_3-integrals being functions of the distance and of the angle, are able to describe the physical behaviour of the interaction of two line sources (charges and forces), since they represent the fundamental and necessary quantities, that is, the interaction force, interaction energy and total torque produced by the interaction of these two line sources.

Relativistic spacetimes admitting almost Schouten solitons

In this paper, we investigate almost Schouten solitons and almost gradient Schouten solitons in spacetimes of general relativity. At first, it is proven that if a generalized Robertson–Walker spacetime permits an almost Schouten soliton, then it becomes a perfect fluid spacetime as well as the spacetime represents a dark matter era. Besides this, we investigate almost gradient Schouten solitons in generalized Robertson–Walker spacetimes. Moreover, a spacetime obeying almost Schouten solitons whose potential vector field is a non-homothetic conformal vector field is of Petrov type [Formula: see text] or [Formula: see text].

Transverse Dynamics of Two-Dimensional Traveling Periodic Gravity–Capillary Water Waves

We study the transverse dynamics of two-dimensional traveling periodic waves for the gravity–capillary water-wave problem. The governing equations are the Euler equations for the irrotational flow of an inviscid fluid layer with free surface under the forces of gravity and surface tension. We focus on two open sets of dimensionless parameters (alpha ,beta ), where alpha and beta are the inverse square of the Froude number and the Weber number, respectively. For each arbitrary but fixed pair (alpha ,beta ) in one of these sets, two-dimensional traveling periodic waves bifurcate from the trivial constant flow. In one open set we find a one-parameter family of periodic waves, whereas in the other open set we find two geometrically distinct one-parameter families of periodic waves. Starting from a transverse spatial dynamics formulation of the governing equations, we investigate the transverse linear instability of these periodic waves and the induced dimension-breaking bifurcation. The two results share a common analysis of the purely imaginary spectrum of the linearization at a periodic wave. We apply a simple general criterion for the transverse linear instability problem and a Lyapunov center theorem for the dimension-breaking bifurcation. For parameters (alpha ,beta ) in the open set where there is only one family of periodic waves, we prove that these waves are linearly transversely unstable. For the other open set, we show that the waves with larger wavenumber are transversely linearly unstable. We also identify an open subset of parameters for which both families of periodic waves are transversely linearly unstable. For each of these transversely linearly unstable periodic waves, a dimension-breaking bifurcation occurs in which three-dimensional doubly periodic waves bifurcate from the two-dimensional periodic wave.