Front propagation in geometric and phase field models of stratified media

We study front propagation problems for forced mean curvature flows and their phase field variants that take place in stratified media, i.e., heterogeneous media whose characteristics do not vary in one direction. We consider phase change fronts in infinite cylinders whose axis coincides with the symmetry axis of the medium. Using the recently developed variational approaches, we provide a convergence result relating asymptotic in time front propagation in the diffuse interface case to that in the sharp interface case, for suitably balanced nonlinearities of Allen-Cahn type. The result is established by using arguments in the spirit of $\Gamma$-convergence, to obtain a correspondence between the minimizers of an exponentially weighted Ginzburg-Landau type functional and the minimizers of an exponentially weighted area type functional. These minimizers yield the fastest traveling waves invading a given stable equilibrium in the respective models and determine the asymptotic propagation speeds for front-like initial data. We further show that generically these fronts are the exponentially stable global attractors for this kind of initial data and give sufficient conditions under which complete phase change occurs via the formation of the considered fronts

Comparison of topologies on *-algebras of locally measurable operators

We consider the locally measure topology $t(\mathcal{M})$ on the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a von Neumann algebra $\mathcal{M}$. We prove that $t(\mathcal{M})$ coincides with the $(o)$-topology on $LS_h(\mathcal{M})=\{T\in LS(\mathcal{M}): T^*=T\}$ if and only if the algebra $\mathcal{M}$ is $\sigma$-finite and a finite algebra. We study relationships between the topology $t(\mathcal{M})$ and various topologies generated by faithful normal semifinite traces on $\mathcal{M}$.Comment: 21 page

Neutral hydrogen in galaxy halos at the peak of the cosmic star formation history

We use high-resolution cosmological zoom-in simulations from the FIRE project to make predictions for the covering fractions of neutral hydrogen around galaxies at z=2-4. These simulations resolve the interstellar medium of galaxies and explicitly implement a comprehensive set of stellar feedback mechanisms. Our simulation sample consists of 16 main halos covering the mass range M_h~10^9-6x10^12 Msun at z=2, including 12 halos in the mass range M_h~10^11-10^12 Msun corresponding to Lyman break galaxies (LBGs). We process our simulations with a ray tracing method to compute the ionization state of the gas. Galactic winds increase the HI covering fractions in galaxy halos by direct ejection of cool gas from galaxies and through interactions with gas inflowing from the intergalactic medium. Our simulations predict HI covering fractions for Lyman limit systems (LLSs) consistent with measurements around z~2-2.5 LBGs; these covering fractions are a factor ~2 higher than our previous calculations without galactic winds. The fractions of HI absorbers arising in inflows and in outflows are on average ~50% but exhibit significant time variability, ranging from ~10% to ~90%. For our most massive halos, we find a factor ~3 deficit in the LLS covering fraction relative to what is measured around quasars at z~2, suggesting that the presence of a quasar may affect the properties of halo gas on ~100 kpc scales. The predicted covering fractions, which decrease with time, peak at M_h~10^11-10^12 Msun, near the peak of the star formation efficiency in dark matter halos. In our simulations, star formation and galactic outflows are highly time dependent; HI covering fractions are also time variable but less so because they represent averages over large areas.Comment: 20 pages, including 11 figures. MNRAS, in pres

Instabilities and disorder of the domain patterns in the systems with competing interactions

The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at certain temperatures the ordered hexagonal pattern becomes unstable with respect to the two types of instabilities: the radially-nonsymmetric distortions of the domains and the repumping of the order parameter between the neighbors. Both these instabilities may lead to the transformation of the regular hexagonal pattern into a disordered pattern.Comment: ReVTeX, 4 pages, 3 figures (postscript); submitted to Phys. Rev. Let

Non-meanfield deterministic limits in chemical reaction kinetics far from equilibrium

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte-Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.Comment: 4 pages, 4 figures (submitted to Phys. Rev. Lett.

Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films

We analyze the electric current and magnetic field driven domain wall motion in perpendicularly magnetized ultrathin ferromagnetic films in the presence of interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and in-plane uniaxial anisotropies. We obtain exact analytical Walker-type solutions in the form of one-dimensional domain walls moving with constant velocity due to both spin-transfer torques and out-of-plane magnetic field. These solutions are embedded into a larger family of propagating solutions found numerically. Within the considered model, we find the dependencies of the domain wall velocity on the material parameters and demonstrate that adding in-plane anisotropy may produce domain walls moving with velocities in excess of 500 m/s in realistic materials under moderate fields and currents.Comment: 6 pages, 2 figure

Direct Evidence of Two Superconducting Gaps in FeSe0.5_{0.5}Te0.5_{0.5}: SnS-Andreev Spectroscopy and Lower Critical Field

We present direct measurements of the superconducting order parameter in nearly optimal FeSe$_{0.5}$Te$_{0.5}$ single crystals with critical temperature $T_C \approx 14$ K. Using intrinsic multiple Andreev reflection effect (IMARE) spectroscopy and measurements of lower critical field, we directly determined two superconducting gaps, $\Delta_L \approx 3.3 - 3.4$ meV and $\Delta_S \approx 1$ meV, and their temperature dependences. We show that a two-band model fits well the experimental data. The estimated electron-boson coupling constants indicate a strong intraband and a moderate interband interaction