Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction

A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.Comment: Typos in the solutions are correcte

HV discharge acceleration by sequences of UV laser filaments with visible and near-infrared pulses

We investigate the triggering and guiding of DC high-voltage discharges over a distance of 37 cm by filaments produced by ultraviolet (266 nm) laser pulses of 200 ps duration. The latter reduce the breakdown electric field by half and allow up to 80% discharge probability in an electric field of 920 kV/m. This high efficiency is not further increased by adding nanosecond pulses in the Joule range at 532 nm and 1064 nm. However, the latter statistically increases the guiding length, thereby accelerating the discharge by a factor of 2. This effect is due both to photodetachment and to the heating of the plasma channel, that increases the efficiency of avalanche ionization and reduces electron attachment and recombination.Comment: 12 pages, 6 figure

Nonequilibrium Modeling of the Elementary Step in PDZ3 Allosteric Communication

While allostery is of paramount importance for protein signaling and regulation, the underlying dynamical process of allosteric communication is not well understood. PDZ3 domain represents a prime example of an allosteric single-domain protein, as it features a well-established long-range coupling between the C-terminal $\alpha_3$-helix and ligand binding. In an intriguing experiment, Hamm and coworkers employed photoswitching of the $\alpha_3$-helix to initiate a conformational change of PDZ3 that propagates from the C-terminus to the bound ligand within 200 ns. Performing extensive nonequilibrium molecular dynamics simulations, the modeling of the experiment reproduces the measured timescales and reveals a detailed picture of the allosteric communication in PDZ3. In particular, a correlation analysis identifies a network of contacts connecting the $\alpha_3$-helix and the core of the protein, which move in a concerted manner. Representing a one-step process and involving direct $\alpha_3$-ligand contacts, this cooperative transition is considered as elementary step in the propagation of conformational change

Did COVID lockdowns harm entrepreneurship? Not exactly

The prevalent view is that COVID lockdowns have severely harmed entrepreneurship, but have they? Gorgi Krlev, Katharina Scheidgen, Franziska Günzel-Jensen, Miriam Wolf, and Ali Aslan Gümüsay write that physical distancing created new digital spaces and led to unconventional ways of integrating new people, new products, and new purpose into entrepreneurship. They observed instances in which entrepreneurs opened their mind in fundamental ways to provide services which deviated clearly from their original mission

A Framework for the Generation and Dissemination of Drop Size Distribution (DSD) Characteristics Using Multiple Platforms

Proper characterization of the precipitation drop size distribution (DSD) is integral to providing realistic and accurate space- and ground-based precipitation retrievals. Current technology allows for the development of DSD products from a variety of platforms, including disdrometers, vertical profilers and dual-polarization radars. Up to now, however, the dissemination or availability of such products has been limited to individual sites and/or field campaigns, in a variety of formats, often using inconsistent algorithms for computing the integral DSD parameters, such as the median- and mass-weighted drop diameter, total number concentration, liquid water content, rain rate, etc. We propose to develop a framework for the generation and dissemination of DSD characteristic products using a unified structure, capable of handling the myriad collection of disdrometers, profilers, and dual-polarization radar data currently available and to be collected during several upcoming GPM Ground Validation field campaigns. This DSD super-structure paradigm is an adaptation of the radar super-structure developed for NASA s Radar Software Library (RSL) and RSL_in_IDL. The goal is to provide the DSD products in a well-documented format, most likely NetCDF, along with tools to ingest and analyze the products. In so doing, we can develop a robust archive of DSD products from multiple sites and platforms, which should greatly benefit the development and validation of precipitation retrieval algorithms for GPM and other precipitation missions. An outline of this proposed framework will be provided as well as a discussion of the algorithms used to calculate the DSD parameters