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At least 757 records · Page 42

Thermal Transport Model for Heat Sink Design

A document discusses the development of a finite element model for describing thermal transport through microcalorimeter arrays in order to assist in heat-sinking design. A fabricated multi-absorber transition edge sensor (PoST) was designed in order to reduce device wiring density by a factor of four. The finite element model consists of breaking the microcalorimeter array into separate elements, including the transition edge sensor (TES) and the silicon substrate on which the sensor is deposited. Each element is then broken up into subelements, whose surface area subtends 10 10 microns. The heat capacity per unit temperature, thermal conductance, and thermal diffusivity of each subelement are the model inputs, as are the temperatures of each subelement. Numerical integration using the Finite in Time Centered in Space algorithm of the thermal diffusion equation is then performed in order to obtain a temporal evolution of the subelement temperature. Thermal transport across interfaces is modeled using a thermal boundary resistance obtained using the acoustic mismatch model. The document concludes with a discussion of the PoST fabrication. PoSTs are novel because they enable incident x-ray position sensitivity with good energy resolution and low wiring density.

Chervenak, James A.↗

Integration of the Radiation Belt Environment Model Into the Space Weather Modeling Framework

We have integrated the Fok radiation belt environment (RBE) model into the space weather modeling framework (SWMF). RBE is coupled to the global magnetohydrodynamics component (represented by the Block-Adaptive-Tree Solar-wind Roe-type Upwind Scheme, BATS-R-US, code) and the Ionosphere Electrodynamics component of the SWMF, following initial results using the Weimer empirical model for the ionospheric potential. The radiation belt (RB) model solves the convection-diffusion equation of the plasma in the energy range of 10 keV to a few MeV. In stand-alone mode RBE uses Tsyganenko's empirical models for the magnetic field, and Weimer's empirical model for the ionospheric potential. In the SWMF the BATS-R-US model provides the time dependent magnetic field by efficiently tracing the closed magnetic field-lines and passing the geometrical and field strength information to RBE at a regular cadence. The ionosphere electrodynamics component uses a two-dimensional vertical potential solver to provide new potential maps to the RBE model at regular intervals. We discuss the coupling algorithm and show some preliminary results with the coupled code. We run our newly coupled model for periods of steady solar wind conditions and compare our results to the RB model using an empirical magnetic field and potential model. We also simulate the RB for an active time period and find that there are substantial differences in the RB model results when changing either the magnetic field or the electric field, including the creation of an outer belt enhancement via rapid inward transport on the time scale of tens of minutes.

Glocer, A.↗

The Evolution of Remnant Ice at the Lunar South Pole from Diviner Surface Temperature Results

The Diviner lunar radiometer instrument aboard the Lunar Reconnaissance Orbiter mission has revealed large areas of lunar polar terrain with surface temperatures well below 100K. At these temperatures, the sublimation rate of water ice is well below 1 mm per billion years. In contrast, the loss rate at 120K is more than 1 meter of ice in that time consequently volatiles delivered to the coldest locations can be trapped for over 1 Ga, but will be quickly lost from warmer locales. Here we investigate the loss or retention of a layer of ice-bearing regolith at the lunar south poe, assuming contemporary surface temperature conditions and no other loss processes. We use an analytic solution for the one-dimensional diffusion equation of water ice, assuming an isothermal regolith with pore space comparable to mean grain size, 75 micrometers. Only the top meter of soil is assumed to be ice-bearing. We can then calculate the history of ice content with time based on local temperature, and predict what the epithermal neutron output would be in the presence of such a concentration of hydrogen. We compare the present, observed distribution of hydrogen with what one would expect from the temperature-dependent loss or retention of ice for various times since emplacement.

Elphic, Richard C.↗

A Review of the Ginzburg-Syrovatskii's Galactic Cosmic-Ray Propagation Model and its Leaky-Box Limit

Phenomenological models of galactic cosmic-ray propagation are based on a diffusion equation known as the Ginzburg-Syrovatskii s equation, or variants (or limits) of this equation. Its one-dimensional limit in a homogeneous volume, known as the leaky-box limit or model, is sketched here. The justification, utility, limitations, and a typical numerical implementation of the leaky-box model are examined in some detail.

Barghouty, A. F.↗

RITRACKS: A Software for Simulation of Stochastic Radiation Track Structure, Micro and Nanodosimetry, Radiation Chemistry and DNA Damage for Heavy Ions

The code RITRACKS (Relativistic Ion Tracks) has been developed over the last few years at the NASA Johnson Space Center to simulate the effects of ionizing radiations at the microscopic scale, to understand the effects of space radiation at the biological level. The fundamental part of this code is the stochastic simulation of radiation track structure of heavy ions, an important component of space radiations. The code can calculate many relevant quantities such as the radial dose, voxel dose, and may also be used to calculate the dose in spherical and cylindrical targets of various sizes. Recently, we have incorporated DNA structure and damage simulations at the molecular scale in RITRACKS. The direct effect of radiations is simulated by introducing a slight modification of the existing particle transport algorithms, using the Binary‐Encounter‐Bethe model of ionization cross sections for each molecular orbitals of DNA. The simulation of radiation chemistry is done by a step‐by‐step diffusion‐reaction program based on the Green's functions of the diffusion equation]. This approach is also used to simulate the indirect effect of ionizing radiation on DNA. The software can be installed independently on PC and tablets using the Windows operating system and does not require any coding from the user. It includes a Graphic User Interface (GUI) and a 3D OpenGL visualization interface. The calculations are executed simultaneously (in parallel) on multiple CPUs. The main features of the software will be presented.

Plante, I↗

Free-Energy Calculations. A Mathematical Perspective

Ion channels are pore-forming assemblies of transmembrane proteins that mediate and regulate ion transport through cell walls. They are ubiquitous to all life forms. In humans and other higher organisms they play the central role in conducting nerve impulses. They are also essential to cardiac processes, muscle contraction and epithelial transport. Ion channels from lower organisms can act as toxins or antimicrobial agents, and in a number of cases are involved in infectious diseases. Because of their important and diverse biological functions they are frequent targets of drug action. Also, simple natural or synthetic channels find numerous applications in biotechnology. For these reasons, studies of ion channels are at the forefront of biophysics, structural biology and cellular biology. In the last decade, the increased availability of X-ray structures has greatly advanced our understanding of ion channels. However, their mechanism of action remains elusive. This is because, in order to assist controlled ion transport, ion channels are dynamic by nature, but X-ray crystallography captures the channel in a single, sometimes non-native state. To explain how ion channels work, X-ray structures have to be supplemented with dynamic information. In principle, molecular dynamics (MD) simulations can aid in providing this information, as this is precisely what MD has been designed to do. However, MD simulations suffer from their own problems, such as inability to access sufficiently long time scales or limited accuracy of force fields. To assess the reliability of MD simulations it is only natural to turn to the main function of channels - conducting ions - and compare calculated ionic conductance with electrophysiological data, mainly single channel recordings, obtained under similar conditions. If this comparison is satisfactory it would greatly increase our confidence that both the structures and our computational methodologies are sufficiently accurate. Channel conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations.

free energy↗

Diffusion-Reaction Modeling of Cu Migration in CdTe Solar Devices

In this work, we report on development of one-dimensional (1D) finite-difference and two-dimensional (2D) finite-element diffusion-reaction simulators to investigate mechanisms behind Cu-related metastabilities observed in CdTe solar cells [1]. The evolution of CdTe solar cells performance has been studied as a function of stress time in response to the evolution of associated acceptor and donor states. To achieve such capability, the simu-lators solve reaction-diffusion equations for the defect states in time-space domain self-consistently with the free carrier transport. Re-sults of 1-D and 2-D simulations have been compared to verify the accuracy of solutions.

Guo, Da↗

Modular Aquatic Simulation System 1D

MASS1 simulates open channel hydrodynamics and transport in branched channel networks, using cross-section averaged forms of the continuity, momentum, and convection diffusion equations. Thermal energy transport (temperature), including meteorological influences is supported. The thermodynamics of total dissolved gas (TDG) can be directly simulated. MASS1 has been developed over the last 20 years. It is currently being used on DOE projects that require MASS1 to beopen source. Hence, the authors would like to distribute MASS1 in source form.

Source record↗

Katana

Katana is built on the pre-existing MPACT and Futility libraries. Combining those solves with several new ones that are part of Katana, nodal diffusion equations are solved in 3D using pre-tabulated nodal cross sections. 3D coarse mesh finite difference acceleration is applied to accelerate convergence. Feedback effects are accounted for during the course of the solution.

Graham, Aaron M↗

Dark Matter-Electron Interactions Alter the Luminosity and Spectral Index of M87

We investigate the possibility that cosmic-ray electron cooling through dark matter-electron scatterings contributes to the low radiative efficiency observed in radio-loud galaxies such as M87. Light dark matter can scatter efficiently off electrons in M87, lowering the observed bolometric luminosity compared to astrophysical expectations. This consideration allows us to probe previously unexplored regions of the parameter space of dark matter-electron interactions. We further model the cosmic-ray electron distribution by numerically solving a diffusion equation along the jet and find that efficient dark matter-electron interactions can induce a flattening of the spectral index at different distances from the central supermassive black hole, in better alignment with radio observations from M87.

Hussein, Abdelaziz [MIT] (ORCID:0000000255608668)↗

Solvability of Some Integro-Differential Equations with Anomalous Diffusion in Two Dimensions

We study the existence of solutions of an integro-differential equation in the case of the anomalous diffusion with the negative Laplace operator in a fractional power in two dimensions. The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for non Fredholm elliptic operators in unbounded domains are used.

97 MATHEMATICS AND COMPUTING↗

Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings

In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation

The macroscopic diffusion constant for a charged diffuser is in part dependent on (1) the volume excluded by solute “obstacles” and (2) long-range interactions between those obstacles and the diffuser. Increasing excluded volume reduces transport of the diffuser, while long-range interactions can either increase or decrease diffusivity, depending on the nature of the potential. We previously demonstrated [P. M. Kekenes-Huskey et al., Biophys. J. 105, 2130 (2013)] using homogenization theory that the configuration of molecular-scale obstacles can both hinder diffusion and induce diffusional anisotropy for small ions. As the density of molecular obstacles increases, van der Waals (vdW) and electrostatic interactions between obstacle and a diffuser become significant and can strongly influence the latter's diffusivity, which was neglected in our original model. Here, we extend this methodology to include a fixed (time-independent) potential of mean force, through homogenization of the Smoluchowski equation. We consider the diffusion of ions in crowded, hydrophilic environments at physiological ionic strengths and find that electrostatic and vdW interactions can enhance or depress effective diffusion rates for attractive or repulsive forces, respectively. Additionally, we show that the observed diffusion rate may be reduced independent of non-specific electrostatic and vdW interactions by treating obstacles that exhibit specific binding interactions as “buffers” that absorb free diffusers. Finally, we demonstrate that effective diffusion rates are sensitive to distribution of surface charge on a globular protein, Troponin C, suggesting that the use of molecular structures with atomistic-scale resolution can account for electrostatic influences on substrate transport. This approach offers new insight into the influence of molecular-scale, long-range interactions on transport of charged species, particularly for diffusion-influenced signaling events occurring in crowded cellular environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SU-D-210-04: Using Radiotherapy Biomaterials to Brand and Track Deadly Cancer Cells

Purpose: Metastasis accounts for over 90% of all cancer associated suffering and death and arguably presents the most formidable challenges in cancer management. The detection of metastatic or rare circulating tumor cells (CTCs) in blood or lymph nodes remains a formidable technological challenge. In this study, we investigated the time needed to label each cancer cell in-situ (right at the source tumor) with sufficient number of GNPs that will allow enhanced non-invasive detection via photoacoustic imaging in the lymph nodes. Such in-situ labeling can be achieved via sustained release of the GNPs from Radiotherapy (RT) biomaterials (e.g. fiducials, spacers) coated/loaded with the GNP. Methods: The minimum concentration (1000 GNPs/cell for 50nm GNPs) to detect GNPs with photoacoustic imaging method was experimentally measured by Mallidi et al. and fixed at the tumor sub-volume periphery. In this work, the GNPs were assumed to diffuse from a point source, placed in the middle of a 2–3cm tumor, with an initial concentration of 7–30 mg/g. The time required to label the cells with GNPs was calculated by solving the three dimensional diffusion-reaction equation analytically. The diffusion coefficient of 10nm GNPs was experimentally determined previously. Stokes-Einstein equation was used to calculate the diffusion coefficients for other sizes (2–50nm) of GNPs. The cellular uptake rate constants for several sizes of GNPs were experimentally measured by Jin et al. Results: The time required to label the cells was found 0.635–15.91 days for 2–50nm GNPs with an initial concentration of 7 mg/g GNPs in a 2 cm tumor; 1.379–34.633 days for 2–50nm GNPs with an initial concentration of 30 mg/g GNPs in a 3cm tumor. Conclusion: Our results highlight new potential for labeling CTCs with GNPs released from smart RT biomaterials (i.e. fiducials or spacers loaded with the GNP) towards enhanced non-invasive imaging/detection via photoacoustic imaging.

60 APPLIED LIFE SCIENCES↗

Series integration of the diaphragm cell transport equation when the diffusion coefficient is a function of concentration

An integral of the form, t = B0 + BL ln(Delta-c) + B1(Delta-c) + B2(Delta-c)-squared + ..., where t is the time and Delta-c is the concentration difference across the frit, is derived in the case of the diaphragm cell transport equation where the interdiffusion coefficient is a function of concentration. The coefficient, B0, is a constant of the integration, while the coefficients, BL, B1, B2,..., depend in general upon the constant, the compartment volumes, and the interdiffusion coefficient and various of its concentration derivatives evaluated at the mean concentration for the cell. Explicit formulas for BL, B1, B2,... are given.

Cain, Judith B.↗