Regularity of Harmonic functions for a class of singular stable-like processes

We consider the system of stochastic differential equations

Scattering of waves from nonlinear media with rough surfaces

Abstract

Reflection and scattering of waves from plane and statistically rough interfaces between nonlinear media are studied theoretically. New hysteresis-type dependences of the reflection and transmission coefficients on the amplitude of the incident wave and on the angle of incidence are predicted. Scattering diagrams for diffusely reflected and transmitted fields are calculated. It is found that when the dielectric constant is a steep function of the incident amplitude, nonlinearity suppresses the Bragg resonant scattering mechanism. Smooth roughness of the boundary is shown to enhance the penetration of evanescent waves into nonlinear media.     

Symmetry reduction for molecular dynamics simulation of an imploding gas bubble

We propose a symmetry reduction technique whereby molecular dynamics (MD) simulations for spherically symmetric gas bubbles can be accelerated. Results for an imploding Xenon bubble containing 50 million particles—the smallest measured sonoluminescing system—are presented.     

The submartingale problem for a class of degenerate elliptic operators

We consider the degenerate elliptic operator acting on ${C^2_b}$ functions on [0,∞) ^d : $$\mathcal{L}f(x)=\sum_{i=1}^d a_i(x) x_i^{\alpha_i} \frac{\partial^2 f}{\partial x_i^2} (x) +\sum_{i=1}^d b_i(x) \frac{\partial f}{\partial x_i}(x), $$ where the a _i are continuous functions that are bounded above and below by positive constants, the b _i are bounded and measurable, and the ${\alpha_i\in (0,1)}$ . We impose Neumann boundary conditions on the boundary of [0,∞) ^d . There will not be uniqueness for the submartingale problem corresponding to ${\mathcal{L}}$ . If we consider, however, only those solutions to the submartingale problem for which the process spends 0 time on the boundary, then existence and uniqueness for the submartingale problem for ${\mathcal{L}}$ holds within this class. Our result is equivalent to establishing weak uniqueness for the system of stochastic differential equations $$ {\rm d}X_t^i=\sqrt{2a_i(X_t)} (X_t^i)^{\alpha_i/2}{\rm d}W^i_t + b_i(X_t) {\rm d}t + {\rm d}L_t^{X^i},\quad X^i_t \geq 0, $$ where ${W_t^i}$ are independent Brownian motions and ${L^{X_i}_t}$ is a local time at 0 for X ⁱ .     

The Liouville property and a conjecture of De Giorgi

We consider bounded entire solutions of the nonlinear PDE Δu + u − u³ = 0 in ℝ^d and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes. The proof uses a Liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form operator. © 2000 John Wiley & Sons, Inc.     

Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror

Dramatic spectral narrowing of two normally broadband lasers, Ti:sapphire and Cr:LiSAF, was achieved by simply replacing the output mirror with a reflective, volumetric Bragg grating recorded in photothermal refractive glass. The output power of each laser was unchanged from that obtained using dielectric coated output mirrors with the same output coupling as the Bragg grating while spectral brightness increased by 3 orders of magnitude.     

Micromechanical photothermal spectroscopy of trace gases using functionalized polymers

We demonstrate a novel method to spectroscopically detect and identify trace gases. Micromechanical photothermal spectroscopy (MPS) with functionalized sorbent materials provides trace gas spectra in an optical interaction length of only a few micrometers. We use microcavity interferometry to read out displacements as low as 25 fm/√Hz, heating as low as 200 pW/√Hz, and analyte concentrations as low as 65 parts-per-billion for the nerve agent simulant DMMP. MPS integrated with functional materials represents an important new tool in chip-scale optical sensing.     

Electron stimulated desorption of anions from native and brominated single stranded oligonucleotide trimers

We measured the low energy electron stimulated desorption (ESD) of anions from thin films of native (TXT) and bromine monosubstituted (TBrXT) oligonucleotide trimers deposited on a gold surface (T = thymidine, X = T, deoxycytidine (C), deoxyadenosine (A) or deoxyguanosine (G), Br = bromine). The desorption of H(-), CH(3)(-)/NH(-), O(-)/NH(2)(-), OH(-), CN(-), and Br(-) was induced by 0 to 20 eV electrons. Dissociative electron attachment, below 12 eV, and dipolar dissociation, above 12 eV, are responsible for the formation of these anions. The comparison of the results obtained for the native and brominated trimers suggests that the main pathways of TBrXT degradation correspond to the release of the hydride and bromide anions. Significantly, the presence of bromine in oligonucleotide trimers blocks the electron-induced degradation of nuclobases as evidenced by a dramatic decrease in CN(-) desorption. An increase in the yields of OH(-) is also observed. The debromination yield of particular oligonucleotides diminishes in the following order: BrdU?>?BrdA?>?BrdG?>?BrdC. Based on these results, 5-bromo-2(')-deoxyuridine appears to be the best radiosensitizer among the studied bromonucleosides.     

Probing the QCD critical point with relativistic heavy-ion collisions

We utilize an event-by-event relativistic hydrodynamic calculation performed at a number of different incident beam energies to investigate the creation of hot and dense QCD matter near the critical point. Using state-of-the-art analysis and visualization tools we demonstrate that each collision event probes QCD matter characterized by a wide range of temperatures and baryo-chemical potentials, making a dynamical response of the system to the vicinity of the critical point very difficult to isolate above the background.