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At least 487 records · Page 27

AN AB INITIO MODEL FOR COSMIC-RAY MODULATION

A proper understanding of the effects of turbulence on the diffusion and drift of cosmic rays (CRs) is of vital importance for a better understanding of CR modulation in the heliosphere. This study presents an ab initio model for CR modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. This model is solved for solar minimum heliospheric conditions, utilizing boundary values chosen so that model results are in reasonable agreement with spacecraft observations of turbulence quantities in the solar ecliptic plane and along the out-of-ecliptic trajectory of the Ulysses spacecraft. These results are employed as inputs for modeled slab and two-dimensional (2D) turbulence energy spectra. The modeled 2D spectrum is chosen based on physical considerations, with a drop-off at the very lowest wavenumbers. There currently exist no models or observations for the wavenumber where this drop-off occurs, and it is considered to be the only free parameter in this study. The modeled spectra are used as inputs for parallel mean free path expressions based on those derived from quasi-linear theory and perpendicular mean free paths from extended nonlinear guiding center theory. Furthermore, the effects of turbulence on CR drifts are modeled in a self-consistent way, also employing a recently developed model for wavy current sheet drift. The resulting diffusion and drift coefficients are applied to the study of galactic CR protons and antiprotons using a 3D, steady-state CR modulation code, and sample solutions in fair to good agreement with multiple spacecraft observations are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Preliminary Compendium of the Initial Conditions and Evolution of the Fundamental Interactions of SiC with Ag and Pd

Tri-structural isotropic (TRISO) particles are the fuel of choice for very-high temperature reactors. At the core, these spherical particles consist of an inner fuel kernel of UO{sub 2}, UC{sub 2} or a combination of both, which is coated radially outward by successive layers of low density pyrolytic graphite, an inner high density pyrolytic graphite layer, silicon carbide (SiC) and an outer high density pyrolytic graphite layer. SiC is the main diffusion barrier against the release of fission products due to its hardness and high melting point. Irradiation testing of TRISO particles indicates that trace amounts of metallic fission products can damage or potentially escape through the barrier layer. Surrogate experimental studies have previously been performed by various methods seeking to shed light on and explain the diffusion behavior of Ag and Pd. Although some of these experiments have yielded realistic diffusion coefficients the discrepancy of results between different groups is such that the essential details of the diffusive behavior are still to be fully understood. This work aims to understand the fundamental physical and chemical interactions that take place at the interface of SiC and Ag/Pd, and which give rise to the observed diffusion behavior of these metallic species in TRISO particles. Theoretical simulations of the diffusion of Ag through SiC have been exhaustive but typically yield bulk diffusion coefficients that due to the nature of bulk diffusion phenomena (i.e. slow diffusion) the diffusion coefficients are calculated to be orders of magnitude lower than what experimental observations suggest. This in part is due to the difficulty in simulating realistic models that include various polymorphs of SiC, and the dynamical structural transformations that SiC undergoes in the TRISO environment (which are also to be explained). The result is a particularly challenging problem to solve given that the initial conditions of the interactions of Ag and Pd with SiC are difficult to address, both in theoretical models and surrogate experiments. In order to improve these models the approach taken here is to consider fundamental interactions between Ag and SiC that take place in short time scales by varying the initial environmental conditions, i.e. annealing temperature and time, initial amounts of the metallic species (M) Ag, Pd in SiC/M/SiC multilayers. This work aims to understand the fundamental physical and chemical interactions that take place at the interface of SiC and Ag/Pd, and which give rise to the observed diffusion behavior of these metallic species in TRISO particles. In order to do so we have synthesized SiC/Ag/SiC and SiC/Pd/SiC multilayers of various thicknesses by PLD and characterized them using SEM/EDS. Initial results show that upon annealing Ag agglomerates and ruptures the SiC layer to be released. In the case of Pd a strong chemical interaction is deduced from the slow interlayer diffusion and limited release. Further studies using photoelectron spectroscopy and RHEED will be carried out in order obtain detailed information on the chemical and physical transitions that undergo upon annealing of these systems. (authors)

36 MATERIALS SCIENCE↗

A baseline for ensemble-based, time-resolved inflow reconstruction for a single turbine using large-eddy simulations and latent diffusion models

We are interested in reconstructing winds flowing through a turbine on a second-by-second basis over a 10 min window. Previously, we developed a machine learning algorithm that takes in a snapshot of wind speed measurements and generates ensembles of three-dimensional wind field estimates. Here, we use these estimates as initial conditions in large-eddy simulations and reconstruct atmospheric and turbine response dynamic quantities in a synthetic field campaign. In doing so, we establish a baseline for model validation that future time-aware data assimilation techniques will be compared to. In turbine-free case studies, ground truth wind speeds consistently fall within our estimated wind speed distribution for the first 100 s after the simulation start. In simulations with turbines, the wind estimates show a small bias of 0.10 m s 1 and good correlation of 0.80 during the first 100 s. During this window, our estimates of the Blade 1 bending moment and generator power typically span the ground truth, with the estimate of the former performing better overall. In summary, this approach shows promise as a stand-alone technique for reconstructing real-world inflow and turbine dynamics in 1-2 min windows and as a foundation for future time-aware data assimilation techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analytical Solutions of Transient Drift-Diffusion in P-N Junction Pixel Sensors

Radiation detection in applications ranging from high energy physics to medical imaging rely on solid state detectors, often hybrid pixel detectors with (1) reverse biased p-n junction pixel sensors and (2) readout ASICs, attached by flip chip-bonding. Transient signals characteristics are important in, e.g., matching ASIC and sensor design, modeling and optimizing detector parameters and describing timing and charge sharing properties. Currently analytical forms of transient signals are available for only a few limited cases (e.g., drift or diffusion) or for the steady state (which is not relevant for high energy radiation detection). Tools are available for (relatively slow) numerical evaluation of the transient charge transport. We present here the first analytical solutions of partial differential equations de scribing drift-diffusion-recombination charge transport in planar p-n junction sensors in a variety of conditions: (1) undepleted, (2) fully depleted, (3) taking into account the gradual velocity saturation, and (4) overdepleted. We deduce the Green’s functions which can be applied to any detection problem through simple convolution with the initial conditions. We compare the analytical solutions with Monte Carlo simulations and industry standard simulations (Synopsys Sentaurus), demonstrating good agreement. Using the analytical equations enables fast modeling of the influence of various detector parameters on tracking, imaging and timing performance, describing performance and enabling optimizations for different applications. Finally, we illustrate this model with applications in 3D+T (x,y,z,time) photon tracking and 4D+T (x,y,θ,φ,time) relativistic charged particle tracking.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Phase field-volumetric lattice Boltzmann model of ion uptake in porous nuclear waste form materials under continuous flow

The flow field within the mesopores of sorbent particles plays a crucial role in radionuclide diffusion and ion uptake kinetics, thus, impacting the overall performance of porous nuclear waste form materials. To fundamentally understand the influence of microstructures and material properties on the radionuclide absorption and retention processes requires a coupled multi-physics model that considers the advection and diffusion within the flow field, the reaction at liquid-solid interfaces, and finally, the solid-state diffusion within a complex nanoporous medium. Here, this study employs the volumetric lattice Boltzmann method (VLBM) to accurately and efficiently calculate the steady state velocity field inside the mesopores of sorbent particles. The obtained velocity field is then utilized to calculate the advection of ions in the steady flow. A phase field (PF) model of ion uptake is used to describe the reaction occurring at the solid-liquid interface and diffusion inside the porous medium. The integrated PF-VLBM model is verified in terms of the mass conservation and numerical efficiency and validated qualitatively with experimental observation data. Then, it is applied to study the influence of thermodynamic and kinetic properties, as well as flow field conditions on the ion uptake kinetics. The numerical results demonstrate that the ion uptake kinetics in porous particles has three distinct stages, which is in agreement with the observations in continuous flow experiments. In the first stage, the kinetics is predominantly controlled by the flow field and ion diffusivity in the liquid phase. The kinetics in the second stage is primarily governed by ion diffusivity in the solid phase. In the third stage the system reaches a dynamic equilibrium with a net zero uptake flux at the interface. It is also found that porous structures significantly affect the efficiency and capacity of ion uptake. The simulation results can help to understand the physics behind the observed ion uptake kinetics in experiments and to facilitate the development of constitutive equations that can account for heterogeneous microstructures in engineering performance codes.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Hotspots of soil N 2 O emission enhanced through water absorption by plant residue

N 2 O is a highly potent greenhouse gas and arable soils represent its major anthropogenic source. Field-scale assessments and predictions of soil N 2 O emission remain uncertain and imprecise due to the episodic and microscale nature of microbial N 2 O production, most of which occurs within very small discrete soil volumes. Such hotspots of N 2 O production are often associated with decomposing plant residue. Here we quantify physical and hydrological soil characteristics that lead to strikingly accelerated N 2 O emissions in plant residue-induced hotspots. Results reveal a mechanism for microscale N 2 O emissions: water absorption by plant residue that creates unique micro-environmental conditions, markedly different from those of the bulk soil. Moisture levels within plant residue exceeded those of bulk soil by 4–10-fold and led to accelerated N 2 O production via microbial denitrification. The presence of large (Ø >35 μm) pores was a prerequisite for maximized hotspot N 2 O production and for subsequent diffusion to the atmosphere. Understanding and modelling hotspot microscale physical and hydrologic characteristics is a promising route to predict N 2 O emissions and thus to develop effective mitigation strategies and estimate global fluxes in a changing environment.

59 BASIC BIOLOGICAL SCIENCES↗

Design strategies for self-assembly of discrete targets

Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks to hierarchical sequences of intermediates, all the way to the fully addressable limit in which each component is unique. In this paper, we introduce an idealized model of cubic particles with patterned faces that allows self-assembly strategies to be compared and tested. We consider a simple octameric target, starting with the minimal requirements for successful self-assembly and comparing the benefits and limitations of more sophisticated hierarchical and addressable schemes. Simulations are performed using a hybrid dynamical Monte Carlo protocol that allows self-assembling clusters to rearrange internally while still providing Stokes-Einstein-like diffusion of aggregates of different sizes. Our simulations explicitly capture the thermodynamic, dynamic, and steric challenges typically faced by self-assembly processes, including competition between multiple partially completed structures. Self-assembly pathways are extracted from the simulation trajectories by a fully extendable scheme for identifying structural fragments, which are then assembled into history diagrams for successfully completed target structures. For the simple target, a one-component assembly scheme is most efficient and robust overall, but hierarchical and addressable strategies can have an advantage under some conditions if high yield is a priority.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Two-Dimensional Porous Electrode Model for Capacitive Deionization

Here, ion transport in porous conductive materials is of great importance in a variety of electrochemical systems including batteries and supercapacitors. We here analyze the coupling of flow and charge transport and charge capacitance in capacitive deionization (CDI). In CDI, a pair of porous carbon electrodes is employed to electrostatically retain and remove ionic species from aqueous solutions. We here develop and solve a novel unsteady two-dimensional model for capturing the ion adsorption/desorption dynamics in a flow-between CDI system. We use this model to study the complex, nonlinear coupling between electromigration, diffusion, and advection of ions. We also fabricated a laboratory-scale CDI cell which we use to measure the near-equilibrium, cumulative adsorbed salt, and electric charge as a function of applied external voltage. We use these integral measures to validate and calibrate this model. We further present a detailed computational study of the spatiotemporal adsorption/desorption dynamics under constant voltage and constant flow conditions. We show results for low (20 mM KCl) and relatively high (200 mM KCl) inlet ion concentrations and identify effects of ion starvation on desalination. We show that in both cases electromigrative transport eventually becomes negligible and diffusive ion transport reduces the desalination rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetic Model for the Reduction of Cu II Sites by NO + NH 3 and Reoxidation of NH 3 -Solvated Cu I Sites by O 2 and NO in Cu-SSZ-13

In this work, a kinetic model is developed for the reduction of Cu II sites by NO + NH 3 and the reoxidation of NH 3 -solvated Cu I sites by O 2 and NO in Cu-SSZ-13. Fourier transform infrared (FTIR) spectroscopy and spatially resolved capillary inlet mass spectrometry (SpaciMS) measurements during transient reactor experiments are utilized to identify the rate parameters associated with NO + NH 3 RHC (reduction half-cycle), proposed to occur via two distinct pathways involving adsorbed NH 3 and gas-phase NH 3 . The resulting NO + NH 3 RHC model is validated using spatiotemporal N 2 measurements covering a wide range of temperatures (200–450 °C) and space velocities (53,000–640,000 h –1 ). N 2 O formation is observed and modeled during NO + NH 3 RHC, with quantitative validation under standard selective catalytic reduction (SCR) conditions. Experimentally measured enthalpic and entropic changes associated with O 2 adsorption on NH 3 -solvated Cu I (ZCu(NH 3 ) 2 ) complexes [ Kamasamudram, K. Catal. Today 2010 , 151 (3–4), 212-222], along with activation energies estimated computationally for the intercage diffusion of ZCu(NH 3 ) 2 complexes [ Paolucci, C. Science 2017 , 357 (6 354), 898-903], are incorporated into a mean field kinetic model for the low-temperature oxidation half-cycle (OHC). Significant NH 3 release is observed during the isothermal oxidation of Cu I sites, attributed to desorption of NH 3 ligands from NH 3 -solvated Cu II dimers (Z 2 Cu 2 (NH 3 ) 4 O 2 ). Reduction of these dimeric complexes leads to the consumption of one NO/Cu II , contradicting the expected reduction stoichiometry. Inclusion of a global Arrhenius rate for the NO titration of Z 2 Cu 2 (NH 3 ) 4 O 2 complexes provides accurate representations of standard SCR on reduced and oxidized catalysts, predicting transient NO and NH 3 consumption between 150 and 250 °C as a function of hydrothermal aging. Deactivation of low-temperature standard SCR by NH 3 is observed at high NH 3 pressures, modeled via the formation of superoxo amino (ZCu(NH 3 ) 3 OO*) complexes during NH 3 titration of Z 2 Cu 2 (NH 3 ) 4 O 2 complexes [ Negri, C. J. Am. Chem. Soc. 2020 , 142 (37), 15884-15896]. The redox kinetic model presented here provides a foundational description of active site redox during low-temperature standard SCR, combining the recent kinetic, spectroscopic, and computational findings on the mechanism of standard SCR over Cu-SSZ-13.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interaction of Iron with Alumina Refractory Under Flash Ironmaking Conditions

A novel flash ironmaking technology (FIT) based on the direct reduction of iron ore concentrate by a reducing gas such as hydrogen, natural gas, or coal gas has been developed at the University of Utah. A proper choice of refractories is expected to play an important role in the development of FIT and its scale-up. In this work, the interaction of iron with alumina refractory under flash ironmaking conditions has been investigated. A thermodynamic basis for the interaction phenomena has been developed by considering the Fe-Al-O system, and a kinetic model based on solid-state diffusion is proposed to describe the growth of the hercynite (FeAl{sub 2}O{sub 4}) spinel formed as a result of the interaction between Fe, O (from H{sub 2}O and CO{sub 2}), and Al{sub 2}O{sub 3}. Experiments were conducted with Fe powders and pure Al{sub 2}O{sub 3} in the temperature range 1200 to 1500 °C under gas atmospheres relevant to flash ironmaking, and the reacted samples were analyzed using XRD, SEM-EDX, and EPMA techniques. The analyses of reacted samples confirmed the formation of the hercynite (FeAl{sub 2}O{sub 4}) spinel phase and the thickness of the FeAl{sub 2}O{sub 4} spinel as measured using elemental line scans in SEM-EDX and EPMA varied in the range of 0.5 to 1.3 mm. Results showed that the proposed model suitably describes the growth of the hercynite spinel layer, which obeyed the parabolic rate law at all temperatures. The parabolic rate constants were obtained and the diffusion-controlled growth of the FeAl{sub 2}O{sub 4} layer strongly depended on temperature. Furthermore, using the kinetic model, an expression for the effective diffusivity ( (D{sub eff})-bar ) was obtained and its values at the experimental temperatures were determined. The solid-state diffusion was an activated process, as expected, with an activation energy value of 231 kJ/mol.

36 MATERIALS SCIENCE↗

Grain growth kinetics of the gamma phase metallic uranium

We report metallic uranium is a leading fuel form for sodium cooled fast reactors as an enabling technology of future nuclear energy systems. Mechanistic understanding of fuel behaviors and kinetics under thermodynamic equilibrium and highly non-equilibrium conditions are essential for evaluating fuel performance. It is important to understand and predict the grain and pore evolutions of metallic fuels under thermal and irradiation conditions. However, very limited data are available on the grain growth kinetics and mechanisms of pure gamma phase uranium. In this paper, the pure gamma uranium pellets with different grain structures were fabricated by combining high-energy ball milling and spark plasma sintering. Isothermal annealing tests were performed to investigate the grain growth behavior of the pure gamma phase uranium with different initial grain sizes. A parabolic relationship in grain growth with time was identified for the submicron-sized (374 nm) sample. In contrast, for the nano-sized (137 nm) sample, the grain growth shows a linear relationship with time. The activation energies of grain growth were determined as 199.5 KJ/mol and 80.6 KJ/mol for nano-sized and submicron-sized grain structures, respectively. For the nano-sized sample, the rate-control step of grain growth is dominated by the triple-junction migration, in which the grain boundary triple junction drags the grain growth, leading to a higher activation energy than the bulk diffusion. The dominating mechanism for the submicron-sized sample is grain boundary diffusion. The mechanistic understanding and critical data obtained on the kinetics of pure uranium phases will be useful to evaluate fuel behavior under thermodynamic equilibrium conditions and develop a high fidelity model to predict fuel performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Self-similar and diffusive expansion of nonextensive plasmas

Exact analytical self-similar solution is presented for free collisionless expansion of a two-component plasma of inertial ions and nonextensive electrons into vacuum, using the generalized nonextensive velocity distribution for electrons. Furthermore, a hydrodynamic model of plasma expansion in the presence of the ambipolar diffusion caused by collisions among the plasma species, such as electrons and ions, is developed and a Fokker-Planck-like generalized diffusion equation for steady-state expansion of a nonextensive electron-ion plasma is derived. For the case of generalized statistics and in the absence of particle diffusion, the density, velocity, electric potential, and field of expansion profiles are exactly obtained and studied in terms of the self-similar parameter. It is found that superthermal electrons lead to an accelerated expansion of plasma compared to that of Maxwellian electrons. It is also revealed that the nonextensivity parameter plays a fundamental role on the density, velocity, electric potential, and field configuration of the expansion. Therefore, one is able to distinguish three different regimes q < 1, q = 1, and q > 1 for expansion corresponding to sub-nonextensive, extensive, and super-nonextensive statistical profiles for electrons, respectively. Current research can provide useful information and suggests techniques for investigation of the involved statistical mechanism on the role of the energetic electron fluid in the expansion of plasma in strong pulsed laser-matter interaction experiments. It is also shown that the particle diffusion expansion mechanism becomes more dominant for relatively large values of the nonextensivity parameter, q.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A simple model of multiphoton micromachining in silk hydrogels

High resolution three-dimensional voids can be directly written into transparent silk fibroin hydrogels using ultrashort pulses of near-infrared (NIR) light. Here, we propose a simple finite-element model that can be used to predict the size and shape of individual features under various exposure conditions. We compare predicted and measured feature volumes for a wide range of parameters and use the model to determine optimum conditions for maximum material removal. The simplicity of the model implies that the mechanism of multiphoton induced void creation in silk is due to direct absorption of light energy rather than diffusion of heat or other photoproducts, and confirms that multiphoton absorption of NIR light in silk is purely a 3-photon process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two-temperature effects in Hall-MHD simulations of the HIT-SI experiment

A two-temperature Hall-magnetohydrodynamic (Hall-MHD) model, which evolves the electron and ion temperatures separately, is implemented in the PSI-Tet 3D MHD code and used to model plasma dynamics in the Helicity Injected Torus–Steady Inductive (HIT-SI) experiment. The two-temperature model is utilized for HIT-SI simulations in both the PSI-Tet and NIMROD codes at a number of different injector frequencies in the 14.5–68.5 kHz range. At all frequencies, the NIMROD two-temperature model results in increased toroidal current, lower chord-averaged density, higher average temperatures, outward radial shift of the current centroid, and axial symmetrization of the current centroid, relative to the single-temperature NIMROD simulations. The two-temperature PSI-Tet model illustrates similar trends, but at high frequency operation, it exhibits lower electron temperature, smaller toroidal current, and decreased axial symmetrization with respect to the single-temperature PSI-Tet model. With all models, average temperatures and toroidal currents increase with the injector frequency. Power balance and heat fluxes to the wall are calculated for the two-temperature PSI-Tet model and illustrate considerable viscous and compressive heating, particularly at high injector frequency. Parameter scans are also presented for artificial diffusivity, wall temperature, and density. Both artificial diffusivity and the density boundary condition significantly modify the plasma density profiles, leading to larger average temperatures, toroidal current, and relative density fluctuations at low densities. As a result, a low density simulation achieves sufficiently high current gain (G > 5) to generate significant volumes of closed flux lasting 1–2 injector periods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

97 MATHEMATICS AND COMPUTING↗

First-Principles Studies of Tritium Species Diffusivity Across the Interfaces of Ni-NiZr Alloy-Zircaloy-4

A tritium producing assembly, also known as tritium producing burnable absorber rods (TPBARs), consists of a metal getter tube located between the cladding and γ-LiAlO2 pellets. The metal getter tube is composed of a nickel (Ni) layer coated on Zircaloy-4. The getter assembly is used to capture tritium (3H) species (mainly 3H2 and 3H2O) generated from γ-LiAlO2 pellets during irradiation. Exploring 3H species (3H2, 3H2O) dissociation on the Ni surface and diffusion in the Ni layer and across the interface of Ni-plated Zircaloy-4 getters can provide insights on tritium transport and retention in the pellets and the getter materials. . In FY25, based on the ideal interface model of Ni-Zircaloy-4 generated in FY24, we will further explore the diffusion pathways of 3H across such Ni-ZrNi-alloy layer-Zircalory-4 interfaces under different conditions, including with oxide/hydroxide clusters on the Ni layer, and impurities located in ZrNi-alloy and Zircalory-4 layers. Due to the size limitation of DFT simulation, we will separate the 3-layer system into 3 sub-systems: Ni-ZrNi interface, ZrNi alloy layer, ZrNi-alloy-Zircaloy-4 interface, and simulate the diffusion barriers for tritium.

diffusion barrier↗

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells’ location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells’ diffusion and immune cells’ influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes’ diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

60 APPLIED LIFE SCIENCES↗

A Model to Account for the Effects of Load Ratio and Hydrogen Pressure on the Fatigue Crack Growth Behavior of Pressure Vessel Steels

A phenomenological model for estimating the effects of load ratio R and hydrogen pressure P H2 on the hydrogen-assisted fatigue crack growth rate (HA–FCGR) behavior in the transient and steady-state regimes of pressure vessel steels is described. The “transient regime” is identified with crack growth within a severely embrittled zone of intense plasticity at the crack tip. The “steady-state” behavior is associated with the crack growing into a region of comparatively lower hydrogen concentration located further away from the crack tip. The model treats the effects of R and P H2 as being functionally separable. In the transient regime, the effects of the hydrogen pressure on the HA–FCGR behavior were negligible but were significant in the steady-state regime. The hydrogen concentration in the steady-state region is modeled as being dependent on the kinetics of lattice diffusion, which is sensitive to pressure. Experimental HA–FCGR data from the literature were used to validate the model. The new model was shown to be valid over a wide range of conditions that ranged between –1 ≤ R ≤ 0.8 and 0.02 ≤ P H2 ≤ 103 MPa for pressure vessel steels.

36 MATERIALS SCIENCE↗