Narrow Results

This aim of this work is to apply three proposed mathematical methods, namely, enhanced simple equation, $(G^{\prime }/G)$-expansion and modified F-expansion to investigate solitary wave solutions for the two recently developed extended Sakovich equations in the context of $(2+1)$- and $(3+1)$-dimensional structures. The equations under this study belong to the category of Korteweg–de Vries (KdV) equations which are widely acknowledged as important components of fluid dynamics. Many scientific fields, including mathematics, physics, soliton theory, plasma physics, biology, chemistry, and nonlinear processes can benefit from the use of these equations. The derived solutions are in the form of Trigonometric, hyperbolic, exponential and rational functions. The Mathematica 13 computational software is used to represent some solutions graphically in two- and three-dimensional for the physical phenomena of concern models. Therefore, our work’s inventiveness is demonstrated by the application of many types of new solutions and newly employed creative ways. This facilitates additional research into nonlinear models that realistically capture important physical processes in daily life.

This paper evaluates the performance of hypercube machines on a computational fluid dynamics problem. Our evaluation focuses on a prototype of a class of widely used fluid dynamics codes, FLO52, written by Antony Jameson, which solves the two-dimensional steady Euler equations describing flow around an airfoil. In this paper, we give a description of FLO52, its hypercube mapping, and the code modifications to increase machine utilization. Results from two hypercube computers (a 16 node iPSC/2, and a 512 node NCUBE/ten) are presented and compared. In addition, we develop a mathematical model of the execution time as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained. Predictions about future hypercubes are made using this timing model.

In the present work, we investigate the ability of recently proposed computational operators to characterize the problem of pattern formation by fluid flow and mass transport in a viscous binary fluid mixture under osmosedimentation. We perform a numerical investigation of these patterns using three computational operators (R² → R), computed from the spatial mass distribution, the streamlines, and the velocity fields. Our main goal is to demonstrate the ability of these computational operators to distinguish different dynamical regimes in the complex patterns arising from the osmosedimentation process.

We perform numerical simulations of a new proposal of laboratory experiment that would allow the transformation of a classical fluid into a quantum-type (super)fluid through the application of a generalized quantum potential. This quantum potential is simulated by using a real time retroactive loop involving a measurement of density, a calculation of the potential in function of the measured density, then an application of the calculated potential through a classical force. This general experimental concept is exemplified here by the case of a nonspreading oscillating wave packet in a harmonic oscillator potential. We find signatures of a quantum-like behavior which are stable against various perturbations. Finally, the feasability of a realization of this concept in an actual plasma experiment is analyzed.

Large-scale molecular dynamics (MD) simulations of freely decaying turbulence in three-dimensional space are reported. Fluid components are defined from the microscopic states by eliminating thermal components from the coarse-grained fields. The energy spectrum of the fluid components is observed to scale reasonably well according to Kolmogorov scaling determined from the energy dissipation rate and the viscosity of the fluid, even though the Kolmogorov length is of the order of the molecular scale.

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder–Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel–Bulkley, Ellis, Ree–Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.

Noncommutative algebra in planar quantum mechanics is shown to follow from 't Hooft's recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a charged particle in a magnetic field with an oscillator potential is shown as dual description of the same phenomenon. Finally, noncommutativity in a fluid dynamical model, analogous to the lowest Landau level problem, is discussed.

In this paper we define a noncommutative (NC) metafluid dynamics.^1,2 We applied the Dirac's quantization to the metafluid dynamics on NC spaces. First class constraints were found which are the same obtained in Ref. 4. The gauge covariant quantization of the nonlinear equations of fields on noncommutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the gauge covariant form. In addition, we show that a particular transformation³ on the usual classical phase space (CPS) leads to the same results as of the ⋆-deformation with ν = 0. Besides, we have shown that an additional term is introduced into the dissipative force due to the NC geometry. This is an interesting feature due to the NC nature induced into model.

We generalize the kinetic theory of fluids, in which the description of fluids is based on the geodesic motion of particles, to spacetimes modeled by Finsler geometry. Our results show that Finsler spacetimes are a suitable background for fluid dynamics and that the equation of motion for a collisionless fluid is given by the Liouville equation, as it is also the case for a metric background geometry. We finally apply this model to collisionless dust and a general fluid with cosmological symmetry and derive the corresponding equations of motion. It turns out that the equation of motion for a dust fluid is a simple generalization of the well-known Euler equations.

Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear perturbations, and we use this map to find knotted fluid solutions, as well as new electromagnetic solutions. We find that knotted solutions of Maxwell electromagnetism are also solutions of more general nonlinear theories, like Born–Infeld, and including ones which contain quantum corrections from couplings with other modes, like Euler–Heisenberg and string theory DBI. Null configurations in electromagnetism can be described as a null pressureless fluid, and from this map we can find null fluid knotted solutions. A type of nonrelativistic reduction of the relativistic fluid equations is described, which allows us to find also solutions of the (nonrelativistic) Euler’s equations.

In this paper, we give a general review on the application of ergodic theory to the investigation of dynamics of the Yang–Mills gauge fields and of the gravitational systems, as well as its application in the Monte Carlo method and fluid dynamics. In ergodic theory the maximally chaotic dynamical systems (MCDS) can be defined as dynamical systems that have nonzero Kolmogorov entropy. The hyperbolic dynamical systems that fulfill the Anosov C-condition belong to the MCDS insofar as they have exponential instability of their phase trajectories and positive Kolmogorov entropy. It follows that the C-condition defines a rich class of MCDS that span over an open set in the space of all dynamical systems. The large class of Anosov–Kolmogorov MCDS is realized on Riemannian manifolds of negative sectional curvatures and on high-dimensional tori. The interest in MCDS is rooted in the attempts to understand the relaxation phenomena, the foundations of the statistical mechanics, the appearance of turbulence in fluid dynamics, the nonlinear dynamics of Yang–Mills field and gravitating $N$-body systems as well as black hole thermodynamics. Our aim is to investigate classical- and quantum-mechanical properties of MCDS and their role in the theory of fundamental interactions.

In this study, the peening behavior of shot particles in a fine particle peening (FPP) process such as velocity and impact angles were analyzed by using a high-speed-camera. Results showed that the velocity of shot particles depended on a peening pressure; the higher the peening pressure, the higher the particle velocity. The particle velocity measured in this study was approximately 120 m/s; this was much higher than that of the conventional shot peening (SP) process. This was because the air resistance of shot particles in the FPP process was higher than that of shot particles in the SP process. In order to discuss the surface modification effect of the FPP process, commercial-grade pure iron treated by the FPP process was characterized by micro-Vickers hardness tester and scanning electron microscope (SEM). Thickness of hardened layer treated with higher peening pressure was much higher than that of the lower pressure treated one. The unique microstructure with stratification patterns, which was harder than that of the other part, was observed near the specimen surface. The reason for the microstructural changes by the FPP treatment was discussed based on the kinetic energy of shot particles.

The Allen–Cahn equation (ACE), which has applications in solid-state physics, imaging, plasma physics, material science and other fields, is one of the most important models of the modern era for describing the dynamics of oil pollution, reaction-diffusion mechanisms, and the mechanics of crystalline solids. By using the $(\frac{1}{G^{\prime }})$-expansion method (GEM) and the Bernoulli sub-ODE schemes, some new traveling wave solutions for the governing model are created in this study (BSODE). The reduced integrable ordinary differential equation is produced using the traveling wave hypothesis. To better understand their behavior, the 3D, contour, and 2D graphs are displayed for a number of fascinating exact solutions. Additionally, we use numerical simulation to confirm the stability of the derived analytical solutions. It results the propagation of temporal soliton for long time of simulation. These results will be used to explain physical phenomenon in crystalline solids and others fields.

The cell membrane is an important organ of living cells, which has a complex structure influenced by the interaction between membrane proteins and cell membrane. On the basis of fluid motion and diffusion interaction, a simple model is proposed to evaluate quantitatively the effects of the protein size and membrane fluid velocity on the lateral diffusion of membrane proteins at the cell membrane. The study shows that the diffusion coefficient is a dominant factor on the lateral diffusion.

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of $\alpha (t)$ and $\beta (t)$ can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where $\alpha (t)$ and $\beta (t)$ are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

A bubble equation of motion close to the solid plane is obtained by using the perturbation method. This bubble equation can explain the phenomena of the reentrant microjet penetrating the bubble produced by the external disturbances if the distance between the bubble center to the solid boundary is small enough as well as the external pressure is large enough. Furthermore, two critical points are found. One critical point is the distance between the bubble center to the solid boundary. The other is external pressure. The critical boundary at which the reentrant microjet can just be produced is given. The critical boundary depends on both the distance between the bubble center to the solid boundary and the ratio of external pressure to the initial pressure of the liquid.

We investigate rescaling transformations for the Vlasov–Poisson and Euler–Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the long time behavior of the solutions and can be applied to other models in kinetic theory (two-dimensional symmetric Vlasov–Poisson system with an external magnetic field), in fluid dynamics (Euler system for gases) and in quantum physics (Schrödinger–Poisson system, nonlinear Schrödinger equation).

It is shown that small volume elements of a perfect esentropic fluid move along geodesic lines of a Riemannian space–time.

Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand the gravity and dynamics of black objects in higher dimensions. We provide evidence that:

(i) The gravitational Gregory–Laflamme instability has a classical counterpart in the Rayleigh–Plateau instability of fluids. Each known feature of the gravitational instability can be accounted for in the fluid model. These features include threshold mode, dispersion relation, time evolution and critical dimension of certain phase transitions. Thus, we argue that black strings break in much the same way as water from a faucet breaks up into small droplets.

(ii) General rotating black holes can also be understood with this analogy. In particular, instability and bifurcation diagrams for black objects can easily be inferred.

This correspondence can and should be used as a guiding tool for understanding and exploring the physics of gravity in higher dimensions.