Collapse of wave fronts in reaction-diffusion systems

In this work we develop and test a methodology for the generation of Born-Oppenheimer potential energy surfaces (PES) for use in vibrational structure calculations. The method relies on the widely used restricted-mode-coupling expansion of the fully coupled potential surface where only up to n or less vibrational coordinates are coupled in the potential. Low-order derivatives of the energy are then used to extrapolate the higher mode-coupling potential terms; derivative information is thus used in a convenient way for the evaluation of higher mode couplings avoiding their explicit calculation on multidimensional grids. The formulation, which is a variant of the popular modified Shepard interpolation, is general for any extrapolation of (n+p)-mode-coupling terms from n-mode couplings and can be applied to the energy or any other molecular property surface for which derivative information is available. The method depends only on analytical parameter-free weight functions that satisfy important limiting conditions and control the contribution from each direction of extrapolation. The procedure has been applied on a representative set of 13 molecules, and its accuracy has been tested using only gradients and using both gradients and Hessians. The results provide evidence for the importance of higher mode couplings and illustrate the cost efficiency of the proposed approach.

This article presents numerical studies on multimode transport in a T-shaped quantum transistor geometry. Solving the time independent Schrödinger equation with adequate boundary conditions we model the current for up to six one-dimensional modes in the T structure. It is found, that independent of the number of modes periodic features dominate the conductivity as a function of gate voltage. Their origin is explained in terms of mode coupling in the stub region of the transistor for which the electron velocity in the waveguide is essential. The results are compared with experimental data.

Flow solutions in the presence of pulsation (e.g. from the heart) are developed. Bessel functions are introduced as an aside. The concepts of shocks and solitary waves (solitons) are then discussed as examples of nonlinear effects. The strategy for dealing with intrinsic nonlinearity is described in terms of mode coupling and the Korteweg–de Vries (KdV) equation.

The dimension of attractor of the 2D g-Navier–Stokes equations

In anomaly-free quantum field theories the integrand in the bosonic functional integral—the exponential of the effective action after integrating out fermions—is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-theory the E 8-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions. In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction of heterotic M-theory on cylinders.

The influence of macro bending in a 50 µm GIMMF is investigated in terms of losses and mode coupling. The results indicate that lower order mode groups are weakly influenced by macro bends.

GaAs/GaAlAs quantum well (QW) structures for graded index (GRIN) near IR injection lasers have been studied by polarization dependent photocurrent spectroscopy in the spectral region of QW transitions and in a wide range of temperatures 20 K <EQ T <EQ 375 K. The photocurrent has been measured under short-circuit conditions for the electric vector of the light wave parallel to the plane of the waveguide (TE) as well as perpendicular to the plane of the waveguide (TM). Distinct edges are observed in the quantum efficiency spectra and attributed to the onset of transitions form the heavy hole to electron and light hole to electron subbands, respectively. The observation of different spectral features in TE and TM spectra is discussed in terms of selection rules and mode coupling into the waveguide. Edge positions are compared with calculations of the well states. Coulomb interaction manifests itself in the occurrence of n equals 1 excitonic lines at the hh1-e1, 1h1-e1 and 1h2-e2 subband edges. Temperature dependent measurements indicate mechanisms for carrier escape form the QW. At intermediate temperatures the photocurrent is thermally activated, an explanation in terms of thermionic emission theory is given, and the justification of assuming thermalized non-equilibrium carriers is discussed for different transitions. The observed activation energy is correlated with the energy scale in the QW. At low temperatures the temperature dependence is weak, carrier escape is explained by tunnelling. At the highest temperatures the quantum efficiency decreases again, this is attributed to the growing influence of recombination.

We use a third-order phase equation associated with the Maxwell-Bloch equations to investigate the behavior of a single-mode semiconductor laser subject to injection and frequency detuning. The weakly nonlinear phase equation is analyzed using standard regular perturbation techniques. We derive an approximate Poincar'e map to study the organization of the ultrasubharmonic periodic orbits when the frequency of the injected beam is a rational multiple of the natural frequency of the free-running laser.

The dynamic rupture process of a thin power-law type non-Newtonian liquid film on a cylinder has been analyzed by investigating the stability to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. A decrease in the cylinder radius will induce a stronger lateral capillary force and thus will accelerate the rupture process. The influence of the power-law exponent on rupture is discussed.

Nonlinear thin film rupture has been analyzed by investigating the stability of tear films to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier-Stokes equations, including a body force term due to van der Waals attractions. The governing equation was solved by the finite difference method as part of an initial value problem for spatial periodic boundary conditions. The rupture of the tear film covering the cornea and the formation of dry spots is an important phenomenon in various pathological states associated with a dry eye.

A qualitative analysis of the mechanical response of rate-dependent media caused by a one-dimensional plane smooth wave front and by a continuous wave front attenuating in the media is performed by an underdetermined system of nonlinear partial differential equations. The analysis reveals that smooth strain, particle velocity, and stress profiles, which the smooth wave front has, are not similar and that the wave front is composed of some partial waves having different properties. The property is represented by a set of strain rate, acceleration, and stress rate. The wave front derived here from the analysis is composed of four different partial waves. The front of the wave front is necessarily a contraction wave in which strain, particle velocity, and stress increase with time, while the rear is a rarefaction wave where they all decrease with time. Between these two wave fronts there are two remaining wave fronts. We call these wave fronts mesocontraction waves I and II. Wave front I is a wave in which stress decreases notwithstanding the increase in strain and particle velocity with time, which is followed by the other, i.e., wave front II, where with time, particle velocity, and stress decrease in spite of the increase in strain. The continuous wave front having continuous and nonsmooth profiles of strain, particle velocity, and stress can also be composed of four waves. These waves possess the same property as the corresponding waves in the smooth wave front mentioned above. The velocities at three boundaries that the waves have are discontinuous. Therefore, these four wave fronts are independent waves, just as a shock wave and a rarefraction wave. Specifically, the front wave, i.e., a contraction wave front is being outrun by a second wave front, the second one is being outrun by a third wave front, and the third is being outrun by a fourth wave front, i.e., a rarefaction wave. We call the second wave front degenerate contraction wave I. We also call the third one degenerate contraction wave II. The stress-strain path and the stress-particle velocity path at a position in a rate-dependent medium which is passed by the continuous wave front are schematically shown.

In this work we study the Polyakov-Quark-Meson model for N_f=2 and N_c=3 in a finite volume with the Functional Renormalization Group in a local potential approximation. We choose for the spatial momentum modes periodic and antiperiodic boundary conditions. Because of the lack of a zero mode in the case of antiperiodic boundary conditions we realize a clearly different behavior of the results. We solve the gap-equations for the Polyakov-loop-variable \Phi and its conjugate \Phi^* for different box sizes L as a function of the temperature $T$ and the chemical potential \mu. With these we calculate the pion decay constant and obtain the phase diagram and the pressure. We also study whether the results converge with increasing truncation order N and whether the finite volume results converge with increasing volume size to those of the infinite volume case. For the case of an infinite volume we further solve the gap-equations on all scales. Therefore, we include for the solution of the flow equation an indirect scale dependence of the Polyakov-loop-variable. With this we extend recent approaches which solve the gap-equations only at the infrared cutoff. We calculate with this several thermodynamic variables like the pressure and the trace anomaly. Additionally, we include a non-zero magnetic field and study the possibility of an inverse magnetic catalysis under variation of T_0 with the magnetic field.

We study the manifestly exotic tetraquark D •• s0 ´cu s dµ and the scalar tetraquark f 0 ´ud ū dµ in SU(3) c anisotropic quenched lattice QCD.We adopt the O´aµ-improved Wilson (clover) fermion compact 4Q resonance is almost unchanged.In HBC, we find a nontrivial 4Q resonance state about 100 MeV below the two-meson threshold in some quark-mass region.Its chiral behavior largely differs from a two-meson scattering state.The scalar tetraquark f 0 ´ud ū dµ is found to have the mass of about 1.1GeV after chiral extrapolation, and seems to correspond to f 0 ´980µ.Then, the manifestly exotic tetraquark D •• s0 ´cu s dµ would exist around 1GeV in the idealized SU(4) f chiral limit.Finally, MEM analysis is applied to obtain the spectral function of the 4Q system.

Using conventional two-dimensional nonlinear shallow water equations and the associated semi-momentum finite difference schemes, the nonlinear interaction between storm surges and tides, caused by eight tropical cyclones of different tracks over the coastal waters of Shanghai is numerically studied in this paper. The contributions of various nonlinear terms in the dynamic equations to the water level heights is diagnostically analyzed in detail. It is shown that the nonlinear bottom friction term is of prime importance in controlling the water level and nonlinear tide-surge interaction. The correction to the water level and storm surge due to tide-surge interaction is significant.

Analytical layered solution of radiation and non–Fourier conduction problems in optically complex media