Straarupmcguire3352

Two distinct types of expansions-away from switching points of the boundary condition and at switching points-are considered. Using the expansions, we express the asymptotic behavior of two-point averages near boundaries in terms of one-point averages. We also consider the strip geometry with mixed boundary conditions and derive the distant-wall corrections to one-point averages near one edge due to the other edge. Finally we confirm the consistency of the predictions obtained with conformal-invariance methods and with boundary-operator expansions, in the the first and second halves of the paper.The influence of odd viscosity of Newtonian fluid on the instability of thin film flowing along an inclined plane under a normal electric field is studied. By odd viscosity, we mean apart from the well-known coefficient of shear viscosity, a classical liquid with broken time-reversal symmetry is endowed with a second viscosity coefficient in biological, colloidal, and granular systems. Under the long wave approximation, a nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion. The effects of the odd viscosity and external electric field are considered in this evolution equation and an analytical expression of critical Reynolds number is obtained. It is interesting to find that, by linear stability analysis, the critical Reynolds number increases with odd viscosity and decreases with external strength of electric field. In other words, odd viscosity has a stable effect and electric field has a destabilized effect on flowing of thin film. In addition, through nonlinear analysis, we obtain a Ginsburg-Landau equation and find that the film has not only the supercritical stability zone and the subcritical instability zone but also the unconditional stability zone and the explosive zone. The variations of each zone with related parameters, such as the strength of electric field, odd viscosity, and Reynolds number, etc., are investigated. The results are conducive to the further development of related experiments.Excitable systems with delayed feedback are important in areas from biology to neuroscience and optics. They sustain multistable pulsing regimes with different numbers of equidistant pulses in the feedback loop. Experimentally and theoretically, we report on the pulse-timing symmetry breaking of these regimes in an optical system. A bifurcation analysis unveils that this originates in a resonance phenomenon and that symmetry-broken states are stable in large regions of the parameter space. These results have impact in photonics for, e.g., optical computing and versatile sources of optical pulses.An electrically driven fluid pumping principle and a mechanism of kinklike distortion of the director field n[over ̂] in the microsized nematic volume has been described. It is shown that the interactions, on the one hand, between the electric field E and the gradient of the director's field ∇n[over ̂], and, on the other hand, between the ∇n[over ̂] and the temperature gradient ∇T arising in a homogeneously aligned liquid crystal microfluidic channel, confined between two infinitely long horizontal coaxial cylinders, may excite the kinklike distortion wave spreading along normal to both cylindrical boundaries. Pracinostat research buy Calculations show that the resemblance to the kinklike distortion wave depends on the value of radially applied electric field E and the curvature of these boundaries. Calculations also show that there exists a range of parameter values (voltage and curvature of the inner cylinder) producing a nonstandard pumping regime with maximum flow near the hot cylinder in the horizontal direction.Perfectly matched layer (PML) boundary conditions are constructed for the Dirac equation and general electromagnetic potentials. A PML extension is performed for the partial differential equation and two versions of a staggered-grid single-cone finite-difference scheme. For the latter, PML auxiliary functions are computed either within a Crank-Nicholson scheme or one derived from the formal continuum solution in integral form. Stability conditions are found to be more stringent than for the original scheme. Spectral properties under spatially uniform PML confirm damping of any out-propagating wave contributions. Numerical tests deal with static and time-dependent electromagnetic textures in the boundary regions for parameters characteristic for topological insulator surfaces. When compared to the alternative imaginary-potential method, PML offers vastly improved wave absorption owing to a more efficient suppression of back-reflection. Remarkably, this holds for time-dependent textures as well, making PML a useful approach for transient transport simulations of Dirac fermion systems.Two-dimensional free surface flows in Hele-Shaw configurations are a fertile ground for exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid-fluid interfaces, significant effort has been expended to determining the physics and forcing that set the linear growth rate. However, linear stability does not always imply nonlinear stability. We demonstrate how the combination of a radial and an azimuthal external magnetic field can manipulate the interfacial shape of a linearly unstable ferrofluid droplet in a Hele-Shaw configuration. We show that weakly nonlinear theory can be used to tune the initial unstable growth. Then, nonlinearity arrests the instability and leads to a permanent deformed droplet shape. Specifically, we show that the deformed droplet can be set into motion with a predictable rotation speed, demonstrating nonlinear traveling waves on the fluid-fluid interface. The most linearly unstable wave number and the combined strength of the applied external magnetic fields determine the traveling wave shape, which can be asymmetric.During a pandemic, there are conflicting demands that arise from public health and socioeconomic costs. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimize the socioeconomic damage of a lockdown while still containing infections. Our analysis is based on the SIR model, which we analyze using a clock set by the virus. This use of the "virus time" permits a clean mathematical formulation of our problem. We optimize the socioeconomic cost for a fixed health cost and arrive at a strategy for navigating the pandemic. This involves adjusting the level of lockdowns in a controlled manner so as to minimize the socioeconomic cost.