Pressure disturbances and strained premixed flames

A mathematical model is presented for pressure interactions with premixed flames in a prescribed strained velocity field. A stability analysis is carried out including pressure disturbances and an approximate frequency condition obtained. For positive strain the unsteady analysis indicates that the pulsating instability is suppressed. However, for a converging flow (negative strain), the instability is encouraged. Furthermore, the change of the neutral stability boundary in parameter space is explored, showing that a sharp pressure reduction makes the pulsating instability much more accessible.     

Pulsating hydrodynamic instability and thermal coupling in an extended Landau/Levich model of liquid-propellant combustion: I. Inviscid analysis

Hydrodynamic (Landau) instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. In the context of liquid-propellant combustion, such instability has recently been shown to occur for critical values of the pressure sensitivity of the burning rate and the disturbance wavenumber, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. Additionally, however, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. In the present work, we consider the realistic influence of a non-zero temperature sensitivity in the local burning rate on both types of stability thresholds. It is found that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the (disturbance-wavenumber, pressure-sensitivity) plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values, that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a non-steady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.     

强非局域光晶格中空间孤子的脉动传播

根据强非局域结构中空间孤子的演化方程——非局域非线性薛定谔方程,采用分步傅里叶方法,对一维强非局域光晶格结构中空间孤子的脉动传播进行数值研究.分析了孤子的初始光束能量、非局域程度、光晶格调制强度、光晶格周期以及线性折射率的纵向调制率与空间孤子的脉动传播周期之间的关系,并对影响脉动传播的内在物理机制进行了讨论.同时,还研究了在线性折射率纵向调制情况下强非局域光晶格结构中空间孤子传输的开关行为. 关键词： 非局域非线性薛定谔方程 光晶格 空间孤子 光开关     

脉动流血液通栓的晶格玻尔兹曼模型

本文把血浆看为水,红细胞当作密度为水的悬浮刚性小球,模拟脉动流在锥形管的中的通栓.首先在一定的压积和压差下,在锥形管中产生稳定的栓塞,然后用脉动流来通栓.改变脉动流的频率研究脉动流通栓的条件.     

Lattice-controlled modulation instability in photorefractive feedback systems

We study the modulation instability in a two-dimensional nonlinear single feedback system with a photonic lattice and reveal a sharp transition in the instability regimes as the lattice strength is increased. For a shallow lattice, the instability modes are enhanced parallel to the lattice wave vector, while in stronger lattices, these modes are suppressed.     

A CONCENTRATED MASS ON THE SPINNING UNCONSTRAINED BEAM SUBJECTED TO A THRUST

The dynamic stability of a spinning unconstrained beam subjected to a pulsating follower forceP₀ +P₁cos Ωt is analyzed. A concentrated mass is located at an arbitrary location on the beam, and the stability of the beam is studied with the mass at various locations. The beam is analyzed using the Timoshenko-type shear deformation theory with the rotary inertia. Hamilton's principle is used to derive the equations of motion, and the spinning speed of the beam with various non-dimensional parameters subjected to a pulsating follower force is investigated. The finite element method is applied to analyze the spinning beam model, and the method of multiple scales is used to investigate the dynamic stability characteristics. A pulsating follower force is applied, and then the stability regions are changed with the transitions of the stability area in many regions. The results show that the concentrated mass increases the dynamic stability of the spinning unconstrained beam subjected to a thrust. As the spinning speed of the beam is increased, the instability regions are reduced, but various slight instability regions are additionally developed.     

Behavior of Ising spin glasses in a magnetic field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.     

Diffusive-thermal instabilities of diffusion flames: onset of cells and oscillations

A comprehensive stability analysis of planar diffusion flames is presented within the context of a constant-density model. The analysis provides a complete characterization of the possible patterns that are likely to be observed as a result of differential and preferential diffusion when a planar flame becomes unstable. A whole range of physical parameters is considered, including the Lewis numbers associated with the fuel and the oxidizer, the initial mixture fraction, and the flow conditions. The two main forms of instability are cellular flames, obtained primarily in fuel-lean systems when the Lewis numbers are generally less than one, and planar pulsations, obtained in fuel-rich systems when the Lewis numbers are generally larger than one. The cellular instability is predominantly characterized by stationary cells of characteristic dimension comparable to the diffusion length, but smaller cells that scale on the reaction zone thickness are also possible near extinction conditions. The pulsating instability is characterized by planar oscillations normal to the flame sheet with a well-defined frequency comparable to the reciprocal of the diffusion time; high-frequency modes are also possible just prior to extinction. The analysis also alludes to other possible patterns, such as oscillating cellular structures, which result from competing modes of instability of comparable and/or disparate scales. The expected pattern depends of course on the underlying physical parameters. Consequently, stability boundaries have been identified for the onset of one or another form of the instability. The conditions for the onset of cellular and pulsating flames, as well as the predicted cell size and the frequency of oscillations, compare well with the experimental record.     

On the fast-time oscillatory instabilities of Liñán's diffusion-flame regime

Fast-time instability for diffusion flames, with Lewis numbers set equal for fuel and oxidizer but greater than unity, is numerically analysed by the activation energy asymptotics and Evans function method. The time and length scales being chosen to be those of the inner reactive–diffusive layer, the problem corresponds to the instability problem for the Liñán's diffusion-flame regime. The instability is primarily oscillatory and emerges prior to reaching the turning point of the characteristic C-curve, usually known as the Liñán's extinction condition. A critical Lewis number, L _c , is also found, across which the instability changes its qualitative character. Below L _c , the instability possesses primarily a pulsating nature in that the two real branches of the dispersion relation existing for small wave numbers merge at a finite wave number, from which a pair of complex conjugate branches bifurcate. The maximum growth rate is found at the zero wave number. For Lewis numbers greater than L _c , the eigensolution branch for small reactant leakages is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a travelling nature. As the reactant-leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for 1 < L < L _c . The switching between different instability characters is found to correspond to the Bogdanov-Takens bifurcation.     

Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

To understand the nonlinear dynamical behaviour of a one-dimensional pulsating detonation, results obtained from numerical simulations of the Euler equations with simple one-step Arrhenius kinetics are analysed using basic nonlinear dynamics and chaos theory. To illustrate the transition pattern from a simple harmonic limit-cycle to a more complex irregular oscillation, a bifurcation diagram is constructed from the computational results. Evidence suggests that the route to higher instability modes may follow closely the Feigenbaum scenario of a period-doubling cascade observed in many generic nonlinear systems. Analysis of the one-dimensional pulsating detonation shows that the Feigenbaum number, defined as the ratio of intervals between successive bifurcations, appears to be in reasonable agreement with the universal value of d = 4.669. Using the concept of the largest Lyapunov exponent, the existence of chaos in a one-dimensional unsteady detonation is demonstrated.     

Stability of superflow for ultracold fermions in optical lattices

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.     

Stabilization of optical solitons in chirped PT-symmetric lattices

We investigate the stability properties of optical solitons in a chirped PT-symmetric lattice whose frequency changes in the transverse direction. Linear-stability analysis together with the direct propagation simulations demonstrates that the chirped lattice can improve the stability of optical solitons dramatically. The instability of fundamental solitons can be completely suppressed if the chirp rate exceeds a critical value. A broad stability area of dipole solitons appears if the lattice is appropriately chirped. Thus, we propose an effective way to suppress the instability of solitons in PT-symmetric potentials.     

Different types of nonlinear convective oscillations in a multilayer system under the joint action of buoyancy and thermocapillary effect

The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in a multilayer system, is investigated. The nonlinear convective regimes are studied by the finite difference method. Two different types of boundary conditions – periodic boundary conditions and rigid heat-insulated lateral walls, are considered. It is found that in the case of periodic boundary conditions, the competition of both mechanisms of instability may lead to the development of specific types of flow: buoyant-thermocapillary traveling wave and pulsating traveling wave. In the case of rigid heat-insulated boundaries, various types of nonlinear flows – symmetric and asymmetric oscillations, have been found.     

Lattice Boltzmann Simulation of One Particle Migrating in a Pulsating Flow in Microvessel

A lattice Boltzmann model of two dimensions is used to simulate the movement of a single rigid particle suspended in a pulsating flow in micro vessel.
The particle is as big as a red blood cell, and the micro vessel is four times as wide as the diameter of the particle. It is found that Segré-Silberberg effect will not respond to the pulsation of the flow when the Reynolds number is relatively high. However, when the Reynolds number is low enough, Segré-Silberberg effect disappears. In the steady flow, different initial position leads to different equilibrium positions. In a pulsating flow, different frequencies of pulsation also cause different equilibrium positions. Particularly, when the frequency of pulsation is closed to the human heart rate, Segré-Silberberg effect presents again. The evolutions of velocity, rotation, and trajectory of the particle are investigated to find the dynamics of such abnormal phenomenon.     

Charge density wave in graphene: Magnetic-field-induced Peierls instability

We suggest that a magnetic-field-induced Peierls instability accounts for the recent experiment of Zhang et al. in which unexpected quantum Hall plateaus were observed at high magnetic fields in graphene on a substrate. This Peierls instability leads to an out-of-plane lattice distortion resulting in a charge density wave (CDW) on sublattices A and B of the graphene honeycomb lattice. We also discuss alternative microscopic scenarios proposed in the literature and leading to a similar CDW ground state in graphene.     

Dissipative optical solitons in the absence of bistability and modulation instability

Transversely one-dimensional localized field structures in a wide-aperture interferometer with inertialess nonlinearity of a threshold form are analyzed theoretically for the case when modulation instability of the transversely homogeneous field distributions is absent. It is shown that dissipative solitons exist even in the case of monostability (in the absence of bistability of the homogeneous distributions). In this case, the number of types of solitons turns out to be finite. The possibility of existence of pulsating solitons in an interferometer with inertialess nonlinearity is indicated.     

Modulational Instability of Dipolar Bose-Einstein Condensates in Optical Lattices with Three-Body Interactions

Motivated by the recent experiment [Nature 530(2016) 194] in which a stable droplet in a dipolar quantum gas has been created by the interaction-induced instability, we focus on the modulation instability of an optically-trapped dipolar Bose-Einstein condensate with three-body interaction. Within the mean-field level, we analytically solve the discrete cubic-quintic Gross-Pitaevskii equation with dipole-dipole interaction loaded into a deep optical lattice and show how combined effects of the three-body interaction and dipole-dipole interaction on the condition of modulational instability. Our results show that the interplay of the three-body interaction and dipole-dipole interaction can dramatically change the modulation instability condition compared with the ordinary Gross-Pitaevskii equation. We believe that the predicted results in this work can be useful for the future possible experiment of loading a Bose-Einstein condensate of ~(164)Dy atoms with strong magnetic dipole-dipole interaction into an optical lattice.     

不稳定晶格的能带计算

由于导电高分子是宽能带体系,紧束缚近似下的Su-Schrieffer-Heeger(缩写为SSH)模型存在一系列问题,需要加以改进才能满意地研究导电高分子的一维晶格的不稳定性。本工作将稳定晶格的Wannier函数方法加以推广,用来计算不稳定晶格的电子能带。数值结果表明,本方法的收敛性很快,取到三近邻时,能带的准确度可优于1％。同时能很精确地确定不稳定性所引起的二聚化。 关键词：     

Instabilities in diamond under high shear stress

We investigate, through first-principles calculations, lattice instabilities induced in diamond by the application of high shear stresses. For shear stresses as low as 95 GPa a lattice instability will occur, leading to graphitelike layered structures. This effect is highly anisotropic. The reversal of the direction of the applied shear forces may cause a change of 80 GPa in the shear stress value at which the instability develops. The same reversal also causes different bonds to be broken, resulting in a drastic change in the orientation of the resulting graphitelike structures. We also find that an additional compressive stress of 50 GPa along the (111) direction does not eliminate the shear-induced instability.     

Modulational Instability of Spinor Condensates in an Optical Lattice

We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.