Narrow Results

The paper deals with the mathematical model of movement of a body in a viscous medium. The problem of control for a solid body moving in the viscous medium from initial position to the given one is considered. Movement occurs at Reynolds's greater numbers that generates effects of failure of the laminar boundary layer, caused by return difference of a gradient of pressure. Thus behind a body the vortex path is formed. The frequency of failure of whirlwinds is expressed in the form of the dimensionless parameter. Asymmetrical formation of whirlwinds leads to occurrence periodic cross-section to speed of power influences on a body. Oscillatory movements, especially as a result develop if the frequency of formation of whirlwinds comes nearer to own frequency of fluctuations of a body.

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.

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors, and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e. electrostatic) solvation, non-polar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics, and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace–Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson–Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst–Planck (NP) equations for the dynamics of charged solvent species, generalized Navier–Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent–solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent–solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

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.

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.

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.

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.

The paper proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress–energy tensor for a system with an electromagnetic field leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress–energy tensor expresses relativistic Cauchy’s momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

Solid tumor survives by the process of angiogenesis. In this process micro-vessels are generated around it. Two factors govern this process. One is Tumor Angiogenic Factor (TAF) secreted by the tumor cells and another is tissue Fibronectin (FNT) concentration in the extra-cellular space. These two factors help in mobilization of endothelial cells from nearby blood vessels, a process called angiogenesis. Metronomic chemotherapeutic (MCT) procedure is targeted at this angiogenic microvessels at the cancer milieu and thereby, limits the growth of cancer cells. Here, we have developed a fluid dynamical based analytical model. The model comprises tumor system and a microvasculature system around it. Another characteristic of the developed model is the incorporation of a tracking procedure of either the tumor or microvasculature system from the peripheral blood. Therefore, this analytical method makes a correlation between tumor system, its micro-vasculature system and the peripheral blood circulatory system. With this analytical armamentarium we have tested the effectiveness of MCT in comparison with the conventional maximum tolerable dosing (MTD) strategy. Our simulation result reveals that under the condition MCT is better compared to MTD in controlling tumor growth in a dynamical sense. The advantage of this analytical model is that the tumor system dynamics can be effectively traced through both invasive and non-invasive procedure as and when required.

Few studies are interested in the noninvasive determination of propagation parameters. Reflected waves can be used as an intelligent tool for therapeutic measures. The amplitude and arrival time of reflected wave play an interesting role in investigating cardiovascular diseases. Therefore, this study aims to implement a method based on cepstral analysis for noninvasive decomposition of the incident and reflected waves and determination of local propagation parameters. The cepstral analysis is applied to the blood velocity, which is measured by using phase-contrast magnetic resonance imaging (PCMR) in 20 subjects. The determination of propagation parameters: arrival time, attenuation coefficient, reflection amplitude, and reflection coefficient is based on a mathematical model developed in the previous work. To evaluate the precision of the proposed approach, we focused on the effect of age. In addition, we intended to compare the obtained results to those obtained by the wave intensity analysis (WIA) method. A statistical test analysis was conducted to establish the relationship between the propagation parameters and the age. Our experimental results showed that there is no significant difference in terms of propagation parameters with age ($p>0.05$). Our experimental results correlated with reference values reported in previous studies conducted on the internal arterial carotid. The propagate parameters obtained by the proposed method varied slightly with age. Moreover, the reflection coefficient detected using our proposed method was close to that detected using WIA. We can conclude that the technique described in this paper offers a promising and efficient approach to separating measured velocity waveforms into their incident and reflected components noninvasively.

We discuss the most general Finsler spacetime geometry obeying the cosmological symmetry group SO(4). On this background geometry we derive the equations of motion for the most general kinetic fluid obeying the same cosmological symmetry. For this purpose we propose a set of coordinates on the tangent bundle of the spacetime manifold which greatly simplifies the cosmological symmetry generators.

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.

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 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).

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.

Background: Many cardiovascular diseases modified the arterial wall stiffness. Objectives: This work focuses on the quantification of the elastic biomechanical properties of the internal carotid (ICA) wall by applying the cepstral analysis on healthy volunteers aged from 22 to 86 years old. The purpose of this study is to compare two methods of measurement of arterial compliance ($C)$, arterial distensibility ($D)$, arterial elastance (Eh), and Young’s modulus ($E)$. Material and methods: First, arterial compliance and arterial distensibility were measured in function of wave speed ($c)$, which is measured in our previous works by using two methods. Second, elastance Eh was estimated through the ratio between diastolic radius ($R)$ and $C$. Finally, $E$ was estimated from a statistical study from the literature on h due to the difficulty of measuring wall thickness ($h)$. Results: The Student test demonstrated that there is a very significant difference between young and old subjects in terms of elastance, compliance, and Young’s modulus ($p<0.001$). These findings are in agreement with the reference values reported in the literature. They are very satisfying for distinguishing a pathological change in parietal elasticity. Conclusion: The in vivo application of these methods presents their potential for clinical measurement of arterial stiffness.

The one-dimensional Navier–Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier–Stokes are identical to those obtained from the lubrication approximation within a nondimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.

It has been difficult to predict various classes of boom-and-bust economic cycles and these cyclic catastrophes systematically, because they are related to several biological phenomena. In this report, we will show that our theory on the morphogenetic process and the brain with a rhythm of about seven beats can explain several economic system cycles, because different types of economic cycles are about seven times the length of the fundamental production cycles or durable periods. We will also outline the spatial structure underlying economic systems on the basis of the fluid dynamic theory that describes subatomic systems, biological systems, human network systems, and stars.