Periodic and localized states in natural doubly diffusive convection

Numerical continuation is used to follow branches of steady doubly diffusive convection in a vertical slot driven by imposed horizontal temperature and concentration gradients. No-slip boundary conditions are used on the lateral walls; periodic boundary conditions with large spatial period are used in the vertical direction. A variety of different states, both spatially periodic and spatially localized, are identified and the profusion of the resulting solution branches is linked to a phenomenon known as homoclinic snaking.     

Different localized states of travelling-wave convection in a rectangular container

We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of the rolls perpendicular to their axes. For a negative enough separation ratio, two types of quite different confined states were documented by applying different control processes. One branch of localized travelling waves survives only in a very narrow band within subcritical regime, while another branch straddles the onset of convection existing both in subcritical and supercritical regions. We elucidated that concentration field and its current are key to understand how confined convection is sustained when conductive state is absolutely unstable. The weak structures in the conducting region are demonstrated too.     

Thermal convection in a rotating binary viscoelastic liquid mixture

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation. In particular, we focus in the Maxwelian case of viscoelastic fluid. We obtain explicit expressions for the convective thresholds in terms of the mixture parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic rigid–rigid boundary conditions.     

一维无序二元固体中电子局域性质的研究

从单电子紧束缚模型的哈密顿量出发，格点能量随机取ε_A和ε_B，只计及格点之间的近程跳跃积分，建立了一维无序二元固体模型. 利用负本征值理论及无限阶微扰理论，对系统电子的本征值和本征态进行了数值计算. 结果表明与一定能量本征值对应的电子波函数只分布在系统的一定范围内，显示了其局域性. 借助传输矩阵方法，计算出电子的局域长度，讨论了局域长度随本征能量和无序度的变化关系，并研究了计入不同范围跳跃积分下，局域长度的变化特征. 关键词： 无序 二元固体 电子态 局域长度     

Unstable periodic solution controlling collision of localized convection cells in binary fluid mixture

We study the collision processes of spatially localized convection cells (pulses) in a binary fluid mixture by the extended complex Ginzburg-Landau equations. Both counter- and co-propagating pulse collisions are examined numerically. For counter-propagating pulse collision, we found a special class of unstable time-periodic solutions that play a critical role in determining the output after collision. The solution profile right after collision becomes close to such an unstable pattern and then evolves along one of the unstable manifolds before reaching a final destination. The origin of such a class of unstable solutions, called scattors, can be traced back to two-peak bound states which are stable in an appropriate parameter regime. They are destabilized, as the parameter is varied, and become scattors which play the role of separators of different dynamic regimes. Delayed feedback control is useful to detect them. Also, there is another regime where the origin of the scattors is different from that of the above case. For co-propagating pulse collision, it is revealed that the result of pulse collision depends on the phase difference between pulses. Moreover, we found that a coalescent pulse keeps a profile of two-peak bound state, which is not observed in the case of counter-propagating pulse collision. Complicated collision dynamics become transparent to some extent from the viewpoint of those unstable objects.     

Optical necklace states in Anderson localized 1D systems

We report on the observation of nonlocalized modes or necklace states of light waves in disordered systems in the Anderson localized regime. The samples consist of positional-disordered binary multilayer systems. Anderson localized modes manifest themselves as narrow high-transmission peaks in the transmission spectrum, whereas the average of the logarithm of the transmission coefficient decreases linearly with thickness. Optical necklace states are observed as modes with a characteristic multiresonance time response and relatively fast decay time.     

3D Large scale Marangoni convection in liquid films

We study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. The work is based on the thin film equation which can be derived from the basic hydrodynamic equations. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic fluid parameters.     

Transient photodecay measurements as a probe of the density of localized states in amorphous semiconductors

We show that structure in the density of localized states of an amorphous semiconductor beyond the apparently ubiquitous exponential band tails yield deviations from the usual power-law decay of the photocurrent, i(t) ∝ t^α?1, which can be described analytically. With our expression, dispersive-transport results can be deconvoluted to provide a spectroscopy of the localized-state distribution when well-defined defect centers and band tails are simultaneously present.     

Plume dynamics in quasi-2D turbulent convection

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10(4) times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness delta, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Peclet number, Pe) with the Rayleigh number (Ra(*)) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa(*) approximately Pe(2) that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu approximately nPe, is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. No-slip solutions exhibit no such organization of the boundary flow and the results appear to agree with Priestley's prediction of Nu approximately Ra(1/3). (c) 1997 American Institute of Physics.     

Polaron-type localized states in ferroelectric ferroelastics

The problem of a charged particle in an improper ferroelectric ferroelastic is considered. The existence of the ground and first excited states of the discrete spectrum is established and their dependence on the parameters of the problem is investigated using a direct variational method.     

2D chaotic quantum states in superlattices

The semiclassical motion of an electron along the axis of a superlattice may be calculated from the miniband dispersion curve. Under a weak electric field the electron executes Bloch oscillations which confines the motion along the superlattice axis. When a magnetic field, tilted with respect to the superlattice axis, is applied the electron orbits become chaotic. The onset of chaos is characterised by a complex mixed stable-chaotic phase space and an extension of the orbital trajectories along the superlattice axis. This delocalisation of the orbits is also reflected in the quantum eigenstates of the system some of which show well-defined patterns of high probability density whose shapes resemble certain semiclassical orbits. This suggests that the onset of chaos will be manifest in electron transport through a finite superlattice. We also propose that these phenomena may be observable in the motion of trapped ultra-cold atoms in an optically induced superlattice potential and magnetic quadrupole potential whose axis is tilted relative to the superlattice axis.     

Oscillatory binary fluid convection in large aspect-ratio containers

Direct numerical simulations of chevrons, blinking states, and repeated transients in binary fluid mixtures with a negative separation ratio heated from below are described. The calculations are performed in two-dimensional containers for experimental parameter values and boundary conditions. Quantitative agreement with the experiments of Kolodner [Phys. Rev. E 47, 1038 (1993)] is obtained, and the origin of the blinking and repeated transient states is elucidated.     

NMR of localized magnetic states in graphene

The NMR relaxation rate is studied on the magnetic states of an impurity in bilayer graphene within a tight-binding scenario. The dependencies of the relaxation rate on temperature, interlayer interaction and also the chemical potential have been considered. Although for low temperatures we observe the usual Korringa relation, a characteristic of the conventional fermions, the rate increases with the increase in temperature and tends to saturate for high temperatures. For small interlayer interactions (t_⊥) the system can be either magnetic or non-magnetic. However for higher t_⊥ we observe the existence of only a pure magnetic state. In graphene this transition is also observed with two cusps related to the magnetic to non-magnetic transition, which modifies to a single hump for higher t_⊥, where the system is purely magnetic for any value of chemical potential.     

Anomalously localized states in the Anderson model

It is demonstrated that anomalously localized states (ALS) in the Anderson model, being lattice specific, are not related to any of the continuous theories. We identify the spatial structure of ALS on a lattice and calculate their likelihood. Analytical results explain peculiarities in previous numerical simulations.     

Determination of localized states in porous silicon

We determined the density of state distribution near the Fermi level in porous silicon from the analysis of the current–voltage (J–V) and the current–thickness (J–T) characteristics in the space-charge-limited-current (SCLC) regime. The distribution exhibits a minimum density at the Fermi level, which is similar to the U-shape-trap-distribution observed in crystalline Si–SiO₂ interface or in amorphous Si. Theoretical analysis well explains both the J–V and the J–L characteristics, which implies that the current flow is entirely controlled by localized states situated at the quasi-Fermi level.     

Cros-relaxation of localized triplet states in diamond

We have performed optically detected spin coherent transient measurements for two distinct localized triplet states in brown colored diamond. The triplet states of interest belong to the N?V center in its ground state and the V?O (or 2.818 eV) center in its photo-excited phosphorescent state, respectively. In this paper we focus on the dynamics of cross-relaxation processes which occur when small magnetic fields are applied in such a way that the defect triplet states of the probed centers are tuned in resonance with other defects in the lattice of different spin temperature. The coherent transients reveal the dynamics of cross-relaxation and pure dephasing processes. A quantitative analysis shows that the observed cross-relaxation arises from magnetic dipolar interactions between the probed defects and randomly distributed other defects in the lattice.