Gravitational mass and energy gradient in the ultra-strong magnetic fields

The paper aims to apply the complex octonion to explore the influence of the energy gradient on the Eötvös experiment, impacting the gravitational mass in the ultra-strong magnetic fields. Until now the Eötvös experiment has never been validated under the ultra-strong magnetic field. It is aggravating the existing serious qualms about the Eötvös experiment. According to the electromagnetic and gravitational theory described with the complex octonions, the ultra-strong magnetic field must result in a tiny variation of the gravitational mass. The magnetic field with the gradient distribution will generate the energy gradient. These influencing factors will exert an influence on the state of equilibrium in the Eötvös experiment. That is, the gravitational mass will depart from the inertial mass to a certain extent, in the ultra-strong magnetic fields. Only under exceptional circumstances, especially in the case of the weak field strength, the gravitational mass may be equal to the inertial mass approximately. The paper appeals intensely to validate the Eötvös experiment in the ultra-strong electromagnetic strengths. It is predicted that the physical property of gravitational mass will be distinct from that of inertial mass.     

A possible model for fifth force

Recent reanalysis of the data of the Eötvös experiment suggested the existence of a new force. We show that a negative energy massive scalar field minimally coupled to gravity in a background Schwarzschild metric naturally leads to a potential which can explain the small anomalous effect in the Eötvös experiment.     

Energy conservation and the principle of equivalence

If the equivalence principle is violated, then observers performing local experiments can detect effects due to their position in an external gravitational environment (preferred-location effects) or can detect effects due to their velocity through some preferred frame (preferred-frame effects). We show that the principle of energy conservation implies a quantitative connection between such effects and structure-dependence of the gravitational acceleration of test bodies (violation of the Weak Equivalence Principle). We analyze this connection within a general theoretical framework that encompasses both non-gravitational local experiments and test bodies as well as gravitational experiments and test bodies, and we use it to discuss specific experimental tests of the equivalence principle, including non-gravitational tests such as gravitational redshift experiments, Eötvös experiments, the Hughes-Drever experiment, and the Turner-Hill experiment, and gravitational tests such as the lunar-laser-ranging “Eötvös” experiment, and measurements of anisotropies and variations in the gravitational constant. This framework is illustrated by analyses within two theoretical formalisms for studying gravitational theories: the PPN formalism, which deals with the motion of gravitating bodies within metric theories of gravity, and the TH?μ formalism that deals with the motion of charged particles within all metric theories and a broad class of non-metric theories of gravity.     

Free-Fall Non-Universality in Quantum Theory

The author shows by embodying the Einstein equivalence principle—local Poincaré invariance—and general covariance in quantum theory that wave-function spreading rules out the universality of free fall, that is, the free-fall trajectory of a quantum (test) particle depends on its internal properties. The author provides a quantitative estimate of the free-fall non-universality in terms of the Eötvös parameter, which turns out to be measurable in atom interferometry.     

Black hole acoustics in the minimal geometric deformation of a de Laval nozzle

The correspondence between sound waves, in a de Laval propelling nozzle, and quasinormal modes emitted by brane-world black holes deformed by a 5D bulk Weyl fluid are here explored and scrutinized. The analysis of sound waves patterns in a de Laval nozzle in the laboratory, reciprocally, is here shown to provide relevant data about the 5D bulk Weyl fluid and its on-brane projection, comprised by the minimal geometrically deformed compact stellar distribution on the brane. Acoustic perturbations of the gas fluid flow in the de Laval nozzle are proved to coincide with the quasinormal modes of black holes solutions deformed by the 5D Weyl fluid, in the geometric deformation procedure. Hence, in a phenomenological Eötvös–Friedmann fluid brane-world model, the realistic shape of a de Laval nozzle is derived and its consequences studied.     

Study of acoustic bubble cluster dynamics using a lattice Boltzmann model

The search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor.A long list of complex phenomena underlies the physics of this problem.In the past decades,the lattice Boltzmann method has emerged as a promising tool to address such complexities.In this regard,we have applied a 121-velocity multiphase lattice Boltzmann model to an asymmetric cluster of bubbles in an acoustic field.A problem as a benchmark is studied to check the consistency and applicability of the model.The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics,as well as the screening effect on an acoustic multibubble medium.It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.     

On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing

A new approach to generate initial conditions for RANS simulations of Rayleigh–Taylor (RT) turbulence is presented. The strategy is to provide profiles of turbulent model variables when it is suitable for the turbulence model to be started, and then use these profiles for the turbulence model initialization. The generation of turbulence model variable profiles is achieved with a two-step process. In the first step, a nonlinear modal model assuming small amplitude initial perturbations, incompressible and inviscid fluids is used to track the growth of modes that exist in a given initial perturbation spectrum, and also modes generated by mode interactions. The amplitude development of each mode represents the penetration distance of the light fluid into the heavy fluid (bubble penetration), for a given mode perturbation. The penetration distance of heavy fluid into the light fluid (spike penetration), for a given mode perturbation, is inferred from the bubble's height by an empirical relation valid for small initial amplitudes, and established by DNS simulations that depend on a nondimensional time, and the density contrast (Atwood number). It is hypothesized that the bubble front position of the RT mixing layer can be approximated by the largest penetration distance among all existing modes. The spike front position is approximated in the same fashion. The nonlinear model is evaluated by comparing the bubble front height evolution predicted by the model against the bubble front height predicted by an incompressible implicit large eddy simulations (ILES) code. Comparisons of results for “top-hat” and two-band initial perturbation spectra at Atwood numbers, A_T =0.3 and A_T =0.5 for the former, and A_T =0.01 and A_T =0.5 for the latter, show reasonable agreement. In the second step, the bubble and spike front positions, their derived velocities, and simplified profiles of the mixture fraction distribution of each fluid between the bubble and spike fronts are used with a two-fluid approximation to derive profiles for the turbulence model variables. When initialized with modal model profiles at start time τ₀, (i.e., the time when the turbulence model variable profiles are inferred from the modal model results), the RANS simulations provide at all times τ>τ₀ profiles that show good agreement with ILES simulations. The procedure for determining the time at which the RANS model should be started is a representative use, other parameters can be used depending on the application. In this paper, for the purpose of demonstration of the full strategy, τ₀ is taken as the time at which the mixing layer growth rate parameter α has reached its asymptotic value in the corresponding ILES simulation.     

On the sublimit solution branches of the stripe patterns formed in counterflow diffusion flames by diffusional–thermal instability

The nonlinear dynamics of striped diffusion flames, formed in a two-dimensional counterflow by diffusional–thermal instability with Lewis numbers sufficiently less than unity, is investigated numerically by examining various two-dimensional flame-structure solutions bifurcating from the one-dimensional steady solution. The Lewis numbers for fuel and oxidizer are identically set to be 0.3, and an overall single-step Arrhenius-type chemical reaction with a Zel'dovich number of 7 is employed as the chemistry model. Particular attention is focused on the flame-stripe solution branches in the sub-extinction regime and on the hysteresis encountered during the transition between different solution branches. In the numerical simulations, a nonlinear solution with eight stripes is first realized from the one-dimensional solution at a Damköhler number slightly greater than the extinction Damköhler number. The eight-stripe solution survives Damköhler numbers much smaller than the extinction Damköhler number until successive bifurcations, leading to the doubling of the pattern wavelength, occur at the subsequent forward-transition conditions. At the first forward-transition Damköhler number occurs the transition to a four-stripe solution, which in turn transits to a two-stripe solution at the second forward-transition Damköhler number, a value somewhat smaller than the first. However, further transition from a two-stripe solution to a one-stripe solution is not always possible even if a one-stripe solution can be accessed independently for particular initial conditions. The Damköhler-number ranges and shapes for the two-stripe and one-stripe solutions are found to be virtually identical, implying that each stripe could be an independent structure if the distance between stripes is sufficiently large. By increasing the Damköhler number, backward transitions can be observed. In comparison with the forward-transition Damköhler numbers, the corresponding backward-transition Damköhler numbers are always much greater, thereby indicating significant hysteresis between the stripe patterns of strained diffusion flames.     

黏性液体中单个气泡上升的形状特性

采用基于Level Set方法的直接数值模拟技术对黏性液体中单个气泡的上升运动进行三维模拟.数值模拟采用拟单相流模型处理气泡内外的气液两相流动,应用Level Set方法捕捉运动气泡的变形.针对Eo数从O(0)～O(2),Mo数从O(-11)～O(2)的流动范围,重点研究了上升气泡的形状特性,并与经典的气泡形状图谱进行了比较.模拟结果表明,上升气泡的形状与无量纲参数(Eo、Mo和Re)密切相关.在高Re的扁椭球区域,数值发现了气泡形状的周期性振荡行为.     

Molecular dynamics study of helium bubble pressure in titanium

In this paper,the pressure state of the helium bubble in titanium is simulated by a molecular dynamics(MD) method.First,the possible helium/vacancy ratio is determined according to therelation between the bubble pressure and helium/vacancy ratio;then the dependences of the helium bubble pressure on the bubble radius at different temperatures are studied.It is shown that the product of the bubble pressure and the radius is approximately a constant,a result justifying the pressure-radius relation predicted by thermodynamics-based theory for gas bubble.Furthermore,a state equation of the helium bubble is established based on the MD calculations.Comparison between the results obtained by the state equation and corresponding experimental data shows that the state equation can describe reasonably the state of helium bubble and thus could be used for Monte Carlo simulations of the evolution of helium bubble in metals.     

Ground state of an exciton in a three-dimensional parabolic quantum dot: Convergent perturbative calculation

Working in the effective-mass approximation, we apply a powerful convergent perturbative technique of Turbiner's to the calculation of the ground state energy and the wave function of an exciton confined to a three-dimensional parabolic quantum dot. Unlike the usual Rayleigh–Schrödinger perturbation theory, Turbiner's approach works well even in the regime of strong coupling and does not require the knowledge of the full solution to the undisturbed problem. The second-order convergent calculation presented below is in excellent agreement with the results of exact numerical simulations for a wide range of system's confinement parameters.     

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

<正>In this paper,an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface,where the surface tension is implemented.The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid,an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface,and an indicator function is introduced to update the fluid properties accurately.The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points,and then the surface tension is directly computed by using the normal vector and curvature of the interface.Two benchmark problems,including Laplace’s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation.Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.     

Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method

The rise of bubbles in viscous liquids is not only a very common process in many industrial applications, but also an important fundamental problem in fluid physics. An improved numerical algorithm based on the front tracking method, originally proposed by Tryggvason and his co-workers, has been validated against experiments over a wide range of intermediate Reynolds and Bond numbers using an axisymmetric model [J. Hua, J. Lou, Numerical simulation of bubble rising in viscous liquid, J. Comput. Phys. 22 (2007) 769–795]. In the current paper, this numerical algorithm is further extended to simulate 3D bubbles rising in viscous liquids with high Reynolds and Bond numbers and with large density and viscosity ratios representative of the common air–water two-phase flow system. To facilitate the 3D front tracking simulation, mesh adaptation is implemented for both the front mesh on the bubble surface and the background mesh. On the latter mesh, the governing Navier–Stokes equations for incompressible, Newtonian flow are solved in a moving reference frame attached to the rising bubble. Specifically, the equations are solved using a finite volume scheme based on the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm, and it appears to be robust even for high Reynolds numbers and high density and viscosity ratios. The 3D bubble surface is tracked explicitly using an adaptive, unstructured triangular mesh. The numerical model is integrated with the software package PARAMESH, a block-based adaptive mesh refinement (AMR) tool developed for parallel computing. PARAMESH allows background mesh adaptation as well as the solution of the governing equations in parallel on a supercomputer. Further, Peskin distribution function is applied to interpolate the variable values between the front and the background meshes. Detailed sensitivity analysis about the numerical modeling algorithm has been performed. The current model has also been applied to simulate a number of cases of 3D gas bubbles rising in viscous liquids, e.g. air bubbles rising in water. Simulation results are compared with experimental observations both in aspect of terminal bubble shapes and terminal bubble velocities. In addition, we applied this model to simulate the interaction between two bubbles rising in a liquid, which illustrated the model’s capability in predicting the interaction dynamics of rising bubbles.     

气泡碰壁受力模型和反弹规律

对Mo=10-8~10-12及Re=5~750范围内的上升气泡与壁面垂直碰撞问题进行了理论求解，研究了不同控制参数下气泡碰壁反弹的规律.气泡上升和碰撞过程的运动方程考虑了浮力、液体阻力、附加质量力和与壁面碰撞时引起的薄膜诱导力.气泡碰壁过程气泡界面与壁面形成的液膜厚度变化规律由Stokes-Reynolds方程计算得到.膜内气泡变形引起的流体压强采用Young-Laplace方程求解.结果表明，基于SRYL方程的薄膜诱导力模型可以很好地预测不同Reynolds数下气泡0到多次的反弹轨迹，计算结果与实验结果吻合良好.气泡在碰壁反弹过程中会形成丰富的薄膜形状，如酒窝状变形，丘疹状变形和涟漪状变形.气泡界面变形会引起膜内压强的变化，压强的分布规律与气泡界面形状有着重要的关系.气泡在与壁面碰撞的过程中，薄膜诱导力会起主导作用，且随着Reynolds数的增加薄膜诱导力最大量级增大.气泡碰撞壁面时，反弹次数与Reynolds数有着直接的联系，不同Morton数下的气泡均在相同Reynolds数附近发生气泡反弹次数的变化.      

Axisymmetric bubble pinch-off at high Reynolds numbers

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.     

Numerical simulations for sonochemistry

Numerical simulations for sonochemistry are reviewed including single-bubble sonochemistry, influence of ultrasonic frequency and bubble size, acoustic field, and sonochemical synthesis of nanoparticles. The theoretical model of bubble dynamics including the effect of non-equilibrium chemical reactions inside a bubble has been validated from the study of single-bubble sonochemistry. By the numerical simulations, it has been clarified that there is an optimum bubble temperature for the production of oxidants inside an air bubble such as OH radicals and H₂O₂ because at higher temperature oxidants are strongly consumed inside a bubble by oxidizing nitrogen. Unsolved problems are also discussed.     

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.     

Effect of static pressure on acoustic energy radiated by cavitation bubbles in viscous liquids under ultrasound

The effect of static pressure on acoustic emissions including shock-wave emissions from cavitation bubbles in viscous liquids under ultrasound has been studied by numerical simulations in order to investigate the effect of static pressure on dispersion of nano-particles in liquids by ultrasound. The results of the numerical simulations for bubbles of 5 μm in equilibrium radius at 20 kHz have indicated that the optimal static pressure which maximizes the energy of acoustic waves radiated by a bubble per acoustic cycle increases as the acoustic pressure amplitude increases or the viscosity of the solution decreases. It qualitatively agrees with the experimental results by Sauter et al. [Ultrason. Sonochem. 15, 517 (2008)]. In liquids with relatively high viscosity (～200 mPa s), a bubble collapses more violently than in pure water when the acoustic pressure amplitude is relatively large (～20 bar). In a mixture of bubbles of different equilibrium radius (3 and 5 μm), the acoustic energy radiated by a 5 μm bubble is much larger than that by a 3 μm bubble due to the interaction with bubbles of different equilibrium radius. The acoustic energy radiated by a 5 μm bubble is substantially increased by the interaction with 3 μm bubbles.     

Modulation of the secondary Bjerknes force in multi-bubble systems

The behaviours of insonated bubble clusters are regulated by the secondary Bjerknes force between bubble pairs. While the force has been investigated extensively for two-bubble systems, the modulation of the force by nearby bubbles remains unclear. This problem is investigated in this paper by theoretical analyses and numerical simulations of a three bubble system. For weak oscillations, the third bubble is found to have strong effects when its radius is close to the resonant radius. The equilibrium distance between the bubble pair is reduced when the radius of the third bubble is smaller than the resonant threshold, and increased when it is larger. For strong oscillations of bubbles with radii of a few microns, the third bubble reduces the magnitude of the force, hence increasing the equilibrium distance. The modulation effects depend strongly on the relative sizes of the bubbles. Stronger effects can be produced when the third bubble is placed closer to the smaller bubble in the bubble pair. The findings highlight the need for a more accurate parametrization of the secondary Bjerknes force in the simulation and manipulation of bubble clusters.     

On the characterization of relativistic quantum field theories in terms of finitely many vacuum expectation values. II

The problem of uniqueness of monotone continuous linear extensions of $$T_{(2N)} = \{ 1,T_1 ,...,T_{2N} \} \in E'_{(2N)} = \prod\limits_{n = 0}^{2N} {E'_n } $$ is solved. A characterization of a relativistic QFT in terms of finitely many VEV's is derived. All results are illustrated by an explicit discussion of the extension problem for special cases ofT ₍₄₎={1,0,T ₂,T ₃,T ₄}. This discussion contains explicitly necessary and sufficient conditions onT ₍₄₎ for the existence of minimal extensions and some convenient sufficient conditions.