Time stepping for vectorial operator splitting

We present a fully implicit finite difference method for the unsteady incompressible Navier-Stokes equations. It is based on the one-step θ-method for discretization in time and a special coordinate splitting (called vectorial operator splitting) for efficiently solving the nonlinear stationary problems for the solution at each new time level. The resulting system is solved in a fully coupled approach that does not require a boundary condition for the pressure. A staggered arrangement of velocity and pressure on a structured Cartesian grid combined with the fully implicit treatment of the boundary conditions helps us to preserve the properties of the differential operators and thus leads to excellent stability of the overall algorithm. The convergence properties of the method are confirmed via numerical experiments.     

Modulation of auditory evoked responses to spectral and temporal changes by behavioral discrimination training

Background  

Due to auditory experience, musicians have better auditory expertise than non-musicians. An increased neocortical activity during auditory oddball stimulation was observed in different studies for musicians and for non-musicians after discrimination training. This suggests a modification of synaptic strength among simultaneously active neurons due to the training. We used amplitude-modulated tones (AM) presented in an oddball sequence and manipulated their carrier or modulation frequencies. We investigated non-musicians in order to see if behavioral discrimination training could modify the neocortical activity generated by change detection of AM tone attributes (carrier or modulation frequency). Cortical evoked responses like N1 and mismatch negativity (MMN) triggered by sound changes were recorded by a whole head magnetoencephalographic system (MEG). We investigated (i) how the auditory cortex reacts to pitch difference (in carrier frequency) and changes in temporal features (modulation frequency) of AM tones and (ii) how discrimination training modulates the neuronal activity reflecting the transient auditory responses generated in the auditory cortex.     

Existence and Uniqueness of Strong Solutions for a Class of Quasi‐Linear Hyperbolic Equations with Order Degeneration

Let k(y) > 0, 𝓁(y) > 0 for y > 0, k(0) = 𝓁(0) = 0 and lim_{y → 0}k(y)/𝓁(y) exists; then the equation L(u) ≔ k(y)u_xx – ∂_y(𝓁(y)u_y) + a(x, y)u_x = f(x, y, u) is strictly hyperbolic for y > 0 and its order degenerates on the line y = 0. Consider the boundary value problem Lu = f(x, y, u) in G, u|_AC = 0, where G is a simply connected domain in ℝ² with piecewise smooth boundary ∂G = AB∪AC∪BC; AB = {(x, 0) : 0 ≤ x ≤ 1}, AC : x = F(y) = ∫^y₀(k(t)/𝓁(t))^1/2dt and BC : x = 1 – F(y) are characteristic curves. Existence of generalized solution is obtained by a finite element method, provided f(x, y, u) satisfies Carathéodory condition and |f(x, y, u)| ≤ Q(x, y) + b|u| with Q ∈ L²(G), b = const > 0. It is shown also that each generalized solution is a strong solution, and that fact is used to prove uniqueness under the additional assumption |f(x, y, u₁) – f(x, y, u₂| ≤ C|u₁ – u₂|, where C = const > 0.     

Formation of polymer microrods in shear flow by emulsification--solvent attrition mechanism

Rodlike polymer particles could have interesting properties and could find many practical applications; however, few methods for the production of such particles are available. We report a systematic study of a droplet shearing process for the formation of polymer rods with micrometer or submicrometer diameter and a length of up to tens of micrometers. The process is based on emulsification of a polymer solution under shear, combined with solvent attrition in the surrounding organic medium. The droplets deform and elongate into cylinders, which solidify when the solvent transfers to the dispersion medium. Stopped flow experiments allow distinguishing all stages of the mechanism. The results are interpreted on the basis of the theory of droplet elongation and breakup under shear. The effects of the viscosity ratio and shear stress are matched against the theoretical expectations. The method is simple, efficient, and scalable, and we demonstrate how it can be controlled and modified. The experimental parameters that allow varying the rod size and aspect ratio include shear rate, medium viscosity, and polymer concentration. Examples of the specific properties of the polymer rods, including self-organization, alignment in external fields and in fluid flows, and stabilization of bubbles, droplets, and capsules, are presented.     

Foam superstabilization by polymer microrods

Few foam systems stabilized by solid particles have been reported, and usually the particles have been used in combination with surfactants. We report how foams can be stabilized solely with a new class of anisotropic particles, hydrophobic polymer microrods of diameter less than 1 mum and length of a few tens of micrometers. The obtained foams were extraordinary stable, retaining a constant volume over many days and even surviving drying of most of the free liquid. The bubbles in these foams were sterically stabilized by dense thick "hairy" layers. The rigid intertwined protective shells around the bubbles did not allow the formation of thin films between them. The lifetime of these foams was orders of magnitude longer than the ones stabilized with typical foaming surfactants such as sodium dodecyl sulfate. The addition of sodium dodecyl sulfate led to hydrophilization of the microrods and suppressed the superstabilization effect. Thus, common foaming agents effectively act as defoamers for the ultrastable foams stabilized by microrods.     

A survey on proper codes

The performance of a linear t-error correcting code over a q-ary symmetric memoryless channel with symbol error probability ε is characterized by the probability that a transmission error will remain undetected. This probability is a function of ε involving the code weight distribution and the weight distribution of the cosets of minimum weight at most t. When the undetectable error probability is an increasing function of ε, the code is called t-proper.

The paper presents sufficient conditions for t-properness and a list of codes known to be proper, many of which have been studied by these sufficient conditions. Special attention is paid to error detecting codes of interest in modern communication.