Elliott G. Holliday, John F. Lindner, William L. Ditto
A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Here we explore some of its infinitely many generalizations to two dimensions, including particles confined to rectangle, elliptic, triangle, and cardioid-shaped boxes, using physics-informed neural networks. In particular, we generalize an unsupervised learning algorithm to find the particles' eigenvalues and eigenfunctions. During training, the neural network adjusts its weights and biases, one of which is the energy eigenvalue, so its output approximately solves the Schrödinger equation with normalized and mutually orthogonal eigenfunctions. The same procedure solves the Helmholtz equation for the harmonics and vibration modes of waves on drumheads or transverse magnetic modes of electromagnetic cavities. Related applications include dynamical billiards, quantum chaos, and Laplacian spectra.
The Particle-Particle-Particle-Mesh algorithm elegantly extends the standard Particle-In-Cell scheme by direct summation of interaction that happens over distances below or around mesh size. Generally, this allows for a more accurate description of Coulomb interactions and improves precision in the prediction of key observables. Nevertheless, most implementations neglect electrostatic boundary conditions for the short-ranged interaction that are directly summed. In this paper a variational description of the Particle-Particle-Particle-Mesh algorithm will be developed for the first time and subsequently used to derive temporally and spatially discrete equations of motion. We show that the error committed by neglecting boundary conditions on the short scale is directly tied to the discretization error induced by the computational grid.
Evolving the size distribution of solid aggregates challenges simulations of young stellar objects. Among other difficulties, generic formulae for stability conditions of explicit solvers provide severe constrains when integrating the coagulation equation for astrophysical objects. Recent numerical experiments have recently reported that these generic conditions may be much too stringent. By analysing the coagulation equation in the Laplace space, we explain why this is indeed the case and provide a novel stability condition which avoids time over-sampling.
Both exposure of stratum corneum to neutral pH buffers and blockade of acidification mechanisms disturb cutaneous permeability barrier homeostasis and stratum corneum integrity/cohesion, but these approaches all introduce potentially confounding variables. To study the consequences of stratum corneum neutralization, independent of hydration, we applied two chemically unrelated superbases, 1,1,3,3-tetramethylguanidine or 1,8-diazabicyclo [5,4,0] undec-7-ene, in propylene glycol:ethanol (7:3) to hairless mouse skin and assessed whether discrete pH changes alone regulate cutaneous permeability barrier function and stratum corneum integrity/cohesion, as well as the responsible mechanisms. Both 1,1,3,3-tetramethylguanidine and 1,8-diazabicyclo [5,4,0] undec-7-ene applications increased skin surface pH in parallel with abnormalities in both barrier homeostasis and stratum corneum integrity/cohesion. The latter was attributable to rapid activation (<20 min) of serine proteases, assessed by in situ zymography, followed by serine-protease-mediated degradation of corneodesmosomes. Western blotting revealed degradation of desmoglein 1, a key corneodesmosome structural protein, in parallel with loss of corneodesmosomes. Coapplication of serine protease inhibitors with the superbase normalized stratum corneum integrity/cohesion. The superbases also delayed permeability barrier recovery, attributable to decreased beta-glucocerebrosidase activity, assessed zymographically, resulting in a lipid-processing defect on electron microscopy. These studies demonstrate unequivocally that stratum corneum neutralization alone provokes stratum corneum functional abnormalities, including aberrant permeability barrier homeostasis and decreased stratum corneum integrity/cohesion, as well as the mechanisms responsible for these abnormalities.
The relationship between broiler breast meat color and pH, moisture content, water-holding capacity (WHC), and emulsification capacity (EC) was investigated. In each of three replicate trials, fillets were collected from three different commercial processing plants according to breast meat lightness (L*) values as follows: lighter than normal (light, L* > 53), normal (48 < L* < 53), and darker than normal (dark, L* < 46). Color values of lightness (L*), redness (a*), and yellowness (b*) were measured at 0 and 24 h after collection. Fillets were then ground and homogenized prior to determining color, pH, moisture, WHC, and EC of the ground meat. There was a significant difference among the three color groups (light, normal, and dark) in L*, a*, pH, WHC, and EC. The L* values of whole raw breast fillets had significant negative correlation coefficients with ground meat EC (-0.9237), pH (-0.9610), and a* (-0.6540). Emulsification capacity had significant positive correlations with pH (0.9572) and water-holding capacity (0.7080). WHC had significant correlations with a* (0.8143), moisture (-0.7647), and pH (0.7963). Lighter-than-normal meat was associated with low pH, high moisture, low EC, and low WHC. These results indicate that wide differences in raw breast meat color exist and that these differences may be used by poultry further processors as an indicator of fillets with altered functional properties.
We present the Eulerian Gaussian beam method in anisotropic media. We derive kinematic and dynamic ray tracing equations based on the level set theory and Eulerian theory using the anisotropic eikonal equation. Compared with the traditional anisotropic Gaussian beam method using ray-centered coordinates, the anisotropic Eulerian Gaussian beam method derived in this work has the following three advantages: (1) it can handle the problem of calculating the distance from the imaging point to the beam point more easily; (2) it allows the travel time and amplitude to be distributed uniformly within the actual computational domain without interpolation; (3) it can handle late arrivals, both theoretically and in calculations, due entirely to ray tracing in the phase space.
In this work we demonstrate the usage of the VegasFlow library on multidevice situations: multi-GPU in one single node and multi-node in a cluster. VegasFlow is a new software for fast evaluation of highly parallelizable integrals based on Monte Carlo integration. It is inspired by the Vegas algorithm, very often used as the driver of cross section integrations and based on Google's powerful TensorFlow library. In this proceedings we consider a typical multi-GPU configuration to benchmark how different batch sizes can increase (or decrease) the performance on a Leading Order example integration.
A numerical model is developed to study heat, fluid flow and radiation transfers during the interaction between a UV laser beam and copper. Calculations are performed for a laser of Gaussian and Lorentzian shapes of a wavelength of 400nm, a focal spot radius of 50 micrometers and duration of 80 microsec. In order to describe the transient behaviour in and above the copper target, heat and Navier-Stokes equations are linked to Lambert Beer relationship by taking into account the conduction, and the convection phenomena. The resulting equations are schemed by the finite element method. Comparison with the literature showed qualitative and quantitative agreements for Crater depths and transmission profiles for different laser pulse numbers. Then, the effects of the laser fluences, the Gaussian and Lorentzian shapes on temperature, velocities, melting and evaporation phenomena are studied.