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At least 919 records · Page 51

Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations

Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumor tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Response of a stably stratified atmosphere to low-level heating - An application to the heat island problem

Two-dimensional airflow characteristics past a heat island are investigated using both a linear analytic model and a nonlinear numerical model in the context of the response of a stably stratified atmosphere to specified low-level heating in a constant shear flow. Results from the steady-state, linear, analytic solutions exhibit typical flow response fields that gravity waves produce in response to the local heat source in the presence of environmental flow. The magnitude of the perturbation vertical velocity is shown to be much larger in the shear-flow case than in the uniform-flow case. Two distinct flow features are observed for larger heating amplitude (hence, larger nonlinearity factor): the gravity-wave-type response field on the upstream side of the heat island and the strong updraft circulation cell located on the downstream side. As the heating amplitude increases, the updraft circulation cell strengthens and shifts farther downwind. The strong updraft cell is believed to be partly responsible for precipitation enhancement observed on the downstream side of the heat island. It is found that the continuing downwind propagation of the updraft circulation cell is related to basic-state wind speed.

Baik, Jong-Jin↗

Cost function for low-dimensional manifold topology assessment

Abstract In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

42 ENGINEERING↗

A solvable model of a nonlinear extension of quantum mechanics

We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. Here, we hope that this simple example will elucidate some of the issues of interpreting nonlinear generalization of quantum mechanics that have been put forth to resolve questions about quantum measurement theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Classical integrability of root-$T\overline{T}$ flows

The root-$T\overline{T}$ flow was recently introduced as a universal and classically marginal deformation of any two-dimensional translation-invariant field theory. The flow commutes with the (irrelevant) $T\overline{T}$ flow, and it can be integrated explicitly for a large class of actions, leading to nonanalytic Lagrangians reminiscent of the four-dimensional modified-Maxwell theory (ModMax). It is not a priori obvious whether the root-$T\overline{T}$ flow preserves integrability, as is the case for the $T\overline{T}$ flow. In this paper we demonstrate that this is the case for a large class of classical models by explicitly constructing a deformed Lax connection. We discuss the principal chiral model and the nonlinear sigma models on symmetric and semisymmetric spaces, without or with the Wess-Zumino term. We also construct Lax connections for the two-parameter families of theories deformed by both root-$T\overline{T}$ and $T\overline{T}$ for all of these models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Critical spectrum of fluctuations for deconfinement at protoneutron star cores

We study the deconfinement of hadronic matter into quark matter in a protoneutron star focusing on the effects of the finite size on the formation of just deconfined color superconducting quark droplets embedded in the hadronic environment. The hadronic phase is modeled by the nonlinear Walecka model at finite temperature including the baryon octet and neutrino trapping. For quark matter we use an SU(3){sub f} Nambu-Jona-Lasinio model including color superconductivity. The finite size effects on the just deconfined droplets are considered in the frame of the multiple reflection expansion. In addition, we consider that just deconfined quark matter is transitorily out of equilibrium respect to weak interaction, and we impose color neutrality and flavor conservation during the transition. We calculate self-consistently the surface tension and curvature energy density of the quark hadron interphase and find that it is larger than the values typically assumed in the literature. The transition density is calculated for drops of different sizes, and at different temperatures and neutrino trapping conditions. Then, we show that energy density fluctuations are much more relevant for deconfinement than temperature and neutrino density fluctuations. We calculate the critical size spectrum of energy density fluctuations that allows deconfinement as well as the nucleation rate of each critical bubble. We find that drops with any radii smaller than 800 fm can be formed at a huge rate when matter achieves the bulk transition limit of 5-6 times the nuclear saturation density.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Radiation dose and cancer risk to out-of-field and partially in-field organs from radiotherapy for symptomatic vertebral hemangiomas

Purpose: Vertebral hemangiomas (VHs) are the most common benign tumors of the spine that may cause bone resorption. Megavoltage irradiation is usually the treatment of choice for the management of symptomatic VHs. The current study was conducted to estimate the risk for carcinogenesis from radiotherapy of this benign disease on the basis of the calculated radiation doses to healthy organs. Methods: The Monte Carlo N-particle transport code was employed to simulate the irradiation with 6 MV x-rays of a VH presented in the cervical, upper thoracic, lower thoracic, and lumbar spine. The average radiation dose (D{sub av}) received by each critical organ located outside the primarily irradiated area was calculated. Three-dimensional treatment plans were also generated for the VHs occurring at the four different sites of the spinal cord based on patients’ computed tomography data. The organ equivalent dose (OED) to each radiosensitive structure, which was partly encompassed by the applied treatment fields, was calculated with the aid of differential dose–volume histograms. The D{sub av} and the OED values were combined with a linear-no-threshold model and a nonlinear mechanistic model, respectively, to estimate the organ-, age-, and gender-specific lifetime attributable risks (LARs) for cancer development. The estimated risks were compared with the respective nominal lifetime intrinsic risks (LIRs) for the unexposed population. Results: For a standard target dose of 34 Gy, the OED varied from 0.39–5.15 Gy by the organ of interest and the irradiation site. The D{sub av} range for the out-of-field organs was 4.9 × 10{sup −4} to 0.56 Gy. The LAR for the appearance of malignancies in the partially in-field organs after radiotherapy of male and female patients was (0.08%–1.8%) and (0.09%–1.9%), respectively. These risk values were 1.5–15.5 times lower when compared to the respective LIRs. The lifetime probability for out-of-field cancer induction in irradiated males and females was (2.5 × 10{sup −4} to 7.7 × 10{sup −2})% and (1.4 × 10{sup −4} to 2.6 × 10{sup −1})%, respectively. The above risks were one to four orders of magnitude lower than the LIRs. Conclusions: The probability for the development of out-of-field malignancies due to radiotherapy for VHs is trivial with respect to the nominal risk for unexposed population. The respective cancer risks to partially in-field organs are smaller than the nominal probabilities but they should not be considered as inconsiderable. These risks may be taken into account during the follow-up of patients treated for a symptomatic VH.

60 APPLIED LIFE SCIENCES↗

Efficient and Extensible Quasi-Explicit Modular Nonlinear Multiscale Battery Model: GH-MSMD

Complex physics and long computation time hinder the adoption of computer aided engineering models in the design of large-format battery cells and systems. A modular, efficient battery simulation model -- the multiscale multidomain (MSMD) model -- was previously introduced to aid the scale-up of Li-ion material and electrode designs to complete cell and pack designs, capturing electrochemical interplay with 3-D electronic current pathways and thermal response. Here, this paper enhances the computational efficiency of the MSMD model using a separation of time-scales principle to decompose model field variables. The decomposition provides a quasi-explicit linkage between the multiple length-scale domains and thus reduces time-consuming nested iteration when solving model equations across multiple domains. In addition to particle-, electrode- and cell-length scales treated in the previous work, the present formulation extends to bus bar- and multi-cell module-length scales. We provide example simulations for several variants of GH electrode-domain models.

30 DIRECT ENERGY CONVERSION↗

Calibrating the SPECTACULAR constitutive model using legacy Sandia data for two filled epoxy systems: 828/CTBN/DEA/GMB and 828/DEA/GMB

The SPECTACULAR model is a development extension of the Simplified Potential Energy Clock (SPEC) model. Both models are nonlinear viscoelastic constitutive models used to predict a wide range of time-dependent behaviors in epoxies and other glass-forming materials. This report documents the procedures used to generate SPECTACULAR calibrations for two particulate-filled epoxy systems, 828/CTBN/DEA/GMB and 828/DEA/GMB. No previous SPECTACULAR or SPEC calibration exists for 828/CTBN/DEA/GMB, while a legacy SPEC calibration exists for 828/DEA/GMB. To generate the SPECTACULAR calibrations, a step-by-step procedure was executed to determine parameters in groups with minimal coupling between parameter groups. This procedure has often been deployed to calibrate SPEC, therefore the resulting SPECTACULAR calibration is backwards compatible with SPEC (i.e. none of the extensions specific to SPECTACULAR are used). The calibration procedure used legacy Sandia experimental data stored on the Polymer Properties Database website. The experiments used for calibration included shear master curves, isofrequency temperature sweeps under oscillatory shear, the bulk modulus at room temperature, the thermal strain during a temperature sweep, and compression through yield at multiple temperatures below the glass transition temperature. Overall, the calibrated models fit the experimental data remarkably well. However, the glassy shear modulus varies depending on the experiment used to calibrate it. For instance, the shear master curve, isofrequency temperature sweep under oscillatory shear, and the Young's modulus in glassy compression yield values for the glassy shear modulus at the reference temperature that vary by as much as 15 %. Also, for 828/CTBN/DEA/GMB, the temperature dependence of the glassy shear modulus when fit to the Young's modulus at different temperatures is approximately four times larger than when it is determined from the isofrequency temperature sweep under oscillatory shear. For 828/DEA/GMB, the temperature dependence of the shear modulus determined from the isofrequency temperature sweep under oscillatory shear accurately predicts the Young's modulus at different temperatures. When choosing values for the shear modulus, fitting the glassy compression data was prioritized. The new and legacy calibrations for 828/DEA/GMB are similar and appear to have been calibrated from the same data. However, the new calibration improves the fit to the thermal strain data. In addition to the standard calibrations, development calibrations were produced that take advantage of development features of SPECTACULAR , including an updated equilibrium Helmholtz free energy that eliminates undesirable behavior found in previous work. In addition to the previously mentioned experimental data, the development calibrations require data for the heat capacity during a stress-free temperature sweep to calibrate thermal terms.

36 MATERIALS SCIENCE↗