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At least 523 records · Page 29

Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering

The document presents recent algorithmic and implementation advances of the two-stage robust optimization (RO) solver PyROS, and a benchmarking study which demonstrates the utility of PyROS for two-stage RO problems. The advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the initializations of the subproblems used by the underlying cutting set algorithm, and extensions of the uncertainty set interfaces. The benchmarking study is performed on a library of over 8,500 instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. An amine-based CO2 capture case study is presented to demonstrate the utility of PyROS for large-scale process models. Overall, the results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

Sherman, Jason↗

Self-organization via active exploration in robotic applications. Phase 2: Hybrid hardware prototype

In many environments human-like intelligent behavior is required from robots to assist and/or replace human operators. The purpose of these robots is to reduce human time and effort in various tasks. Thus the robot should be robust and as autonomous as possible in order to eliminate or to keep to a strict minimum its maintenance and external control. Such requirements lead to the following properties: fault tolerance, self organization, and intelligence. A good insight into implementing these properties in a robot can be gained by considering human behavior. In the first phase of this project, a neural network architecture was developed that captures some fundamental aspects of human categorization, habit, novelty, and reinforcement behavior. The model, called FRONTAL, is a 'cognitive unit' regulating the exploratory behavior of the robot. In the second phase of the project, FRONTAL was interfaced with an off-the-shelf robotic arm and a real-time vision system. The components of this robotic system, a review of FRONTAL, and simulation studies are presented in this report.

Oegmen, Haluk↗

Advanced Metal Separation (AMS) via Marangoni Effect-driven Separation

For practical, economical, and sustainable human missions to the Moon, processing of lunar regolith and metal oxides is necessary for localized production of oxygen (O2) and metals that can be repurposed as rocket propellant, life support O2, and in-space manufactured parts. The primary candidates for in-situ resource utilization (ISRU) regolith processing are carbothermic reductions and molten regolith electrolysis (MRE) which both produce oxygen and a reduced, deoxygenated metallic slag. A metal separation technique is still required to capture and purify metals from the deoxygenated slag for reuse in areas such as metallic part fabrication, structural or design frameworks, and metal catalyst production. The Marangoni Effect is best explained as mass transfer along an interface driven by surface tension gradients induced by temperature and concentration differences. Due to the temperature gradients, molten metal can be transported in this fashion to create thin films. This method can transport molten metal in the absence of gravity or mechanical motion and greatly increases the available surface area for a vacuum fractional separation process. In this study, a novel vacuum furnace induces the Marangoni Effect to fractionally decompose and separate valuable metals (e.g., aluminum) from thin films of molten metal via vacuum distillation. The proposed work will examine lunar regolith, metal-based recycling feedstocks, and metallic slags produced from the carbothermal reduction of regolith. Data and observations from this study could produce a simple yet effective method of refining lunar derived metals by taking advantage of the high vacuum environment present on the lunar surface.

ISRU↗

Architectural Framework for Conceptualizing Exploration Class Medical Operations

Currently, discrete projects within NASA’s Human Research Program (HRP) take aim at providing future exploration missions with the capabilities necessary to operate within a progressively Earth-independent operative environment. Realizing an entire ecosystem that can accomplish these goals requires a clear visualization on how each project contributes to the overall objectives of Human Health and Performance (HH&P) in that context. The Exploration Medical Capability (ExMC) Element has developed an architectural framework for exploration class medical operations by utilizing a systems engineering approach using model-based systems engineering (MBSE). This model, a System of Systems Architecture (SoSA), captures a means of integrating various independent but related efforts into a comprehensive view associated with HRP’s goal of providing progressively Earth-Independent Medical Operations (EIMO). This level of visibility is realized by identifying interfaces between development efforts and existing programs that contribute to the overall mission of EIMO even if those extend past the traditional boundary of HRP. Potential interfaces that are considered important when constructing an architecture include program/project Needs, Goals, and Objectives (NGOs), capabilities, envisioned use cases/scenarios, and system/subsystem structure. This presentation will focus on the processes that were used to generate the SoSA along with a means to realize its utility amongst other MBSE products from ExMC. Evaluation of the best architecture moving forward can then be achieved that promotes cohesion between various functional areas of HH&P. Additionally, the SoSA is developed with a long-term vision for the dynamic integration of novel technological developments that may be implemented in the future. The SoSA is intended to enable Stakeholders the ability to view the broader interconnections that exist and begin to create avenues of communication between various efforts. The benefits of a SoSA provide an essential step towards addressing the unique challenges of attaining the goals of broader exploration class medical missions of the future.

Systems engineering↗

Architectural Framework for Conceptualizing Exploration Class Medical Operations

Currently, discrete projects within NASA’s Human Research Program (HRP) take aim at providing future exploration missions with the capabilities necessary to operate within a progressively Earth-independent operative environment. Realizing an entire ecosystem that can accomplish these goals requires a clear visualization on how each project contributes to the overall objectives of Human Health and Performance (HH&P) in that context. The Exploration Medical Capability (ExMC) Element has developed an architectural framework for exploration class medical operations by utilizing a systems engineering approach using model-based systems engineering (MBSE). This model, a System of Systems Architecture (SoSA), captures a means of integrating various independent but related efforts into a comprehensive view associated with HRP’s goal of providing progressively Earth-Independent Medical Operations (EIMO). This level of visibility is realized by identifying interfaces between development efforts and existing programs that contribute to the overall mission of EIMO even if those extend past the traditional boundary of HRP. Potential interfaces that are considered important when constructing an architecture include program/project Needs, Goals, and Objectives (NGOs), capabilities, envisioned use cases/scenarios, and system/subsystem structure. This presentation will focus on the processes that were used to generate the SoSA along with a means to realize its utility amongst other MBSE products from ExMC. Evaluation of the best architecture moving forward can then be achieved that promotes cohesion between various functional areas of HH&P. Additionally, the SoSA is developed with a long-term vision for the dynamic integration of novel technological developments that may be implemented in the future. The SoSA is intended to enable Stakeholders the ability to view the broader interconnections that exist and begin to create avenues of communication between various efforts. The benefits of a SoSA provide an essential step towards addressing the unique challenges of attaining the goals of broader exploration class medical missions of the future.

Systems engineering↗

Loci/STREAM Sharp Interface Model Validation of Cryogenic Propellant Tank Self-Pressurization

This paper documents a model validation effort for the prediction of cryogenic propellant tank selfpressurization physics using the Loci/STREAM sharp interface CFD model developed at NASA MSFC. Cryogenic fluid management (CFM) applications for long duration spaceflight missions require accurate modeling of heat transfer and thermodynamics. Therefore, detailed validation of those physics is important to ensure simulation accuracy. In the past, the MSFC Propulsion Fluid Dynamics Branch has validated and used the Loci/STREAM Volume of Fluid (VOF) module extensively for propellant slosh applications, which are dominated by fluid motion. For cases where the interface gas/liquid interface is essentially static, the Loci/STREAM sharp interface was developed for more rapid and efficient CFM analysis. In the present study, Loci/STREAM sharp interface simulations were compared with the NASA K-site self-pressurization experiment of a flight weight, partially full, LH2 tank in normal gravity. This study investigated several parametric effects and made a number of important observations on the performance of the Loci/STREAM sharp interface method: - First, a homogeneous model was derived to verify the CFD model. The homogeneous model assumes both gas and liquid phases are uniform and are at saturation temperature. The predicted pressure rise rates at 3.5 W/m2 and 2.0 W/m2 with a 49% fill level are all lower than the experimental measurement. This is expected due to the observed temperature stratification near the gas-liquid interface during testing. - The k-w and k-e turbulence models predict comparable pressurization rates, which are much lower than the experiment measurement. On the other hand, the pressure values and pressurization rates from both models are almost the same as those of the homogeneous model. The current turbulence model is too diffusive and is not capable of capturing the thermal stratification in the liquid and ullage. - When using the laminar flow model, the pressurization rate is found to be very close to the experimental value when a quasi-steady flow field is allowed to develop by continuously venting the tank prior to pressurization as was done during testing. On the other hand, without initial venting, the rate is not constant. Additionally, the development time to reach a quasi-steady flow field differed from the experiment due to the lack of turbulent mixing away from the gas-liquid interface that is expected in reality. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 15% of the experimental value for 49% fill level at 3.5 W/m 2 and is within 18% for 2.0 W/m 2 heat loading. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 18% of the experimental value for a 29% fill level and within 15% for an 83% fill level.

H. Q. Yang↗

The Keck keyword layer

Each Keck instrument presents a consistent software view to the user interface programmer. The view consists of a small library of functions, which are identical for all instruments, and a large set of keywords, that vary from instrument to instrument. All knowledge of the underlying task structure is hidden from the application programmer by the keyword layer. Image capture software uses the same function library to collect data for the image header. Because the image capture software and the instrument control software are built on top of the same keyword layer, a given observation can be 'replayed' by extracting keyword-value pairs from the image header and passing them back to the control system. The keyword layer features non-blocking as well as blocking I/O. A non-blocking keyword write operation (such as setting a filter position) specifies a callback to be invoked when the operation is complete. A non-blocking keyword read operation specifies a callback to be invoked whenever the keyword changes state. The keyword-callback style meshes well with the widget-callback style commonly used in X window programs. The first keyword library was built for the two Keck optical instruments. More recently, keyword libraries have been developed for the infrared instruments and for telescope control. Although the underlying mechanisms used for inter-process communication by each of these systems vary widely (Lick MUSIC, Sun RPC, and direct socket I/O, respectively), a basic user interface has been written that can be used with any of these systems. Since the keyword libraries are bound to user interface programs dynamically at run time, only a single set of user interface executables is needed. For example, the same program, 'xshow', can be used to display continuously the telescope's position, the time left in an instrument's exposure, or both values simultaneously. Less generic tools that operate on specific keywords, for example an X display that controls optical instrument exposures, have also been written using the keyword layer.

Conrad, A. R.↗

Modeling Framework for Data Center

This chapter highlights the critical need for advanced modeling of data centers due to their rapidly increasing energy consumption and impact on grid reliability. Driven by the demand for AI applications, data centers are projected to consume a significant portion of US energy by 2028, putting stress on an already challenged power grid. The chapter emphasizes the importance of "fast" time-scale models to understand the dynamic interactions between data centers and the grid, especially given the rapid power fluctuations of AI workloads. It outlines a modeling framework that includes both offline and real-time EMT domain simulations, detailing the necessary representations for various components like utility interfaces, transformers, IT loads, UPS, cooling loads, Battery Energy Storage Systems (BESS), generators, protection systems, and higher-level control systems. While standard simulation tools like PSCAD offer basic models, custom development is often required to accurately capture the unique and fast-changing behaviors of modern data centers. The chapter also discusses key metrics and test cases for validating these models, focusing on transient load responses, protection relay coordination, and demand flexibility. Finally, it addresses the challenges of modeling large-scale data centers, such as computational complexity and the trade-off between model fidelity and practicality, suggesting hybrid modeling approaches as a solution. The overarching goal is to create a robust framework that helps assess data center impacts on grid stability, identify vulnerabilities, and inform the development of standards for reliable integration of these large loads into the bulk power system.

25 ENERGY STORAGE↗

Directional Solidification of Monotectic and Hypermonotectic Aluminum-indium Alloys Under Micron-g

The objective of this program is to analyze the mechanisms involved in the composite solid structure formation obtained from a miscibility gap alloy under microgravity. The metallic system aluminum-indium was chosen for its low critical temperature, broad miscibility gap, and rather well-known thermodynamic properties. The experiment was performed aboard the Salyut-7 spacecraft. The theories of capture of particulates by an advancing front were not able to explain the observations made on SPAR and Salyut-7 experiments. A new model was developed based on the filtration theory considering the globules population: the solid/liquid interface is like a filter of negligible thickness for the globules and its efficiency is limited by a pressure barrier measured for Al-In alloys by ground based experiments. The Materials Experiment Assembly (MEA)-3 experiment was consequently adjusted to take into account the new model. The behavior of the globules in an interacting population on the solid front is, of course, an essential factor in the theory. The theory is at present being completed by results obtained by the Laboratoire d'Aerothermique of Meudon. The hydrodynamic and thermal interactions between pairs of globules placed in a temperature gradient have been calculated showing a large reduction of the Marangoni effect compared to the isolated globule. Physico-chemical properties of metallic liquid interface are currently being investigated.

Potard, C.↗

Hitts Law? A test of the relationship between information load and movement precision

Recent technological developments have made viable a man-machine interface heavily dependent on graphics and pointing devices. This has led to new interest in classical reaction and movement time work by Human Factors specialists. Two experiments were designed and run to test the dependence of target capture time on information load (Hitt's Law) and movement precision (Fitts' Law). The proposed model linearly combines Hitt's and Fitts' results into a combination law which then might be called Hitts' Law. Subjects were required to react to stimuli by manipulating a joystick so as to cause a cursor to capture a target on a CRT screen. Response entropy and the relative precision of the capture movement were crossed in a factorial design and data obtained that were found to support the model.

Zaleski, M.↗

Membrane peptides and their role in protobiological evolution

How simple membrane peptides performed such essential protocellular functions as transport of ions and organic matter across membranes separating the interior of the cell from the environment, capture and utilization of energy, and transduction of environmental signals, is a key question in protobiological evolution. On the basis of detailed, molecular-level computer simulations we explain how these peptides fold at water-membrane interfaces, insert into membranes, self-assemble into higher-order structures and acquire functions. We have investigated the interfacial behavior and folding of several peptides built of leucine and glutamine residues and have demonstrated that many of them tend to adopt ordered structures. Further, we have studied the insertion of an alpha-helical peptide containing leucine (L) and serine (S) of the form (LSLLLSL)3 into a model membrane. The transmembrane state is metastable, and approximately 15 kcal mol(-1) is required to insert the peptide into the membrane. Investigations of dimers formed by (LSLLLSL)3 and glycophorin A demonstrate how the favorable free energy of helix association can offset the unfavorable free energy of insertion, leading to self-assembly of peptide helices in the membrane. An example of a self-assembled structure is the tetrameric transmembrane pore of the influenza virus M2 protein, which is an efficient and selective voltage-gated proton channel. Our simulations explain the gating mechanism and provide guidelines how to re-engineer the channel to act as a simple proton pump. In general, emergence of integral membrane proteins appears to be quite feasible and may be easier to envision than the emergence of water-soluble proteins.

Models, Chemical↗

Mission interactive scenarion studio for autonomous spacecraft

We propose building a Studio enabling the use of diverse existing mission activity and scenario patterns, the creation of new ones, and the modeling of their effects using existing modeling tools. The core of the Studio is a component-based Type Library, which captures years of mission adaptation patterns in various forms. The Studio works as a content server to capture the developed adaptation knowledge for reuse and provides bridging into different mission uplink implementations, including the Mission Data System [l] (MDS) state/goal machinery. Various activities can be coordinated, controlled, and reused through the Studio's component interface to establish and model a mission scenario. A special component Factory mechanism will be in place to facilitate the adaptation of projects into the Studio. The architecture of the Studio reflects and enforces a division of knowledge and actions into three parts: Model, Controller, Viewer. The Model contains information about (a proposed version of) the spacecraft and mission. The Controller contains logic for constructing scenarios of mission activities. The information in the Model and Controller is principally in the form of reusable patterns. A Viewer can be a simple or complex software system. For example, Apgen [2,3] is one possible viewer, MDS is another. A 3-tiered infrastructure is used for the Studio, reflecting the Model, Controller, Viewer architecture [4,5]. The Studio is useful in pre-phase A of a project by enabling spacecraft design options to be played against desired mission scenarios. In later design phases of a project, the construction and modeling of more detailed scenarios is supported by the Studio.

autonomous spacecraft↗

Centering a DDR Strobe in the Middle of a Data Packet

The Orion CEV Northstar ASIC (application- specific integrated circuit) project required a DDR (double data rate) memory bus driver/receiver (DDR PHY block) to interface with external DDR memory. The DDR interface (JESD79C) is based on a source synchronous strobe (DQS\) that is sent along with each packet of data (DQ). New data is provided concurrently with each edge of strobe and is sent irregularly. In order to capture this data, the strobe needs to be delayed and used to latch the data into a register. A circuit solves the need for training a DDR PRY block by incorporating a PVT-compensated delay element in the strobe path. This circuit takes an external reference clock signal and uses the regular clock to calibrate a known delay through a data path. The compensated delay DQS signal is then used to capture the DQ data in a normal register. This register structure can be configured as a FIFO (first in first out), in order to transfer data from the DDR domain to the system clock domain. This design is different in that it does not rely upon the need for training the system response, nor does it use a PLL (phase locked loop) or a DLL (delay locked loop) to provide an offset of the strobe signal. The circuit is created using standard ASIC building blocks, plus the PVT (process, voltage, and temperature) compensated delay line. The design uses a globally available system clock as a reference, alleviating the need to operate synchronously with the remote memory. The reference clock conditions the PVT compensated delay line to provide a pre-determined amount of delay to any data signal that passes through this delay line. The delay line is programmed in degrees of offset, so that one could think of the clock period representing 360deg of delay. In an ideal environment, delaying the strobe 1/4 of a clock cycle (90deg) would place the strobe in the middle of the data packet. This delayed strobe can then be used to clock the data into a register, satisfying setup and hold requirements of the system.

Johnson, Michael↗

Modeling Droplet Heat and Mass Transfer during Spray Bar Pressure Control of the Multipurpose Hydrogen Test Bed (MHTB) Tank in Normal Gravity

A CFD model for simulating pressure control in cryogenic storage tanks through the injection of a subcooled liquid into the ullage is presented and applied to the 1g MHTB spray bar cooling experiments. An Eulerian-Lagrangian approach is utilized to track the spray droplets and capture the interaction between the discrete droplets and the continuous ullage phase. The spray model is coupled with the VOF model by performing particle tracking in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. A new model for calculating the droplet-ullage heat and mass transfer is developed. In this model, a droplet is allowed to warm up to the saturation temperature corresponding to the ullage vapor pressure, after which it evaporates while remaining at the saturation temperature. The droplet model is validated against the results of the MHTB spray-bar cooling experiments with 50% and 90% tank fill ratios. The predictions of the present T-sat based model are compared with those of a previously developed kinetic-based droplet mass transfer model. The predictions of the two models regarding the evolving tank pressure and temperature distributions, as well as the droplets' trajectories and temperatures, are examined and compared in detail. Finally, the ullage pressure and local vapor and liquid temperature evolutions are validated against the corresponding data provided by the MHTB spray bar mixing experiment.

mass transfer↗

Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. In this work, the results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

97 MATHEMATICS AND COMPUTING↗

Operando Surface-Enhanced Infrared Spectroscopy Connects Interfacial Dynamics with Reaction Kinetics During Electrochemical CO 2 Reduction on Copper

The reaction microenvironment plays a key role in dictating the selectivity of electrochemical CO 2 reduction. However, understanding the chemical nature of this microenvironment under operating conditions remains a substantial challenge. For this study, we employed attenuated total reflectance surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS) in operando for simultaneous measurements of reaction kinetics and concentrations of reactants and intermediates at the reaction interface, all under controlled mass transport conditions. These operando measurements enable direct correlations between the reaction microenvironment, mass transport, and kinetics for a Cu electrocatalyst, such as higher local concentrations of CO 2 under faster mass transport corresponding to higher rates of CO 2 reduction. We observed that faster mass transport decreased the *CO coverage at less negative potentials (-0.6 V RHE ) and increased the *CO coverage at more negative potentials (-1.1 V RHE ). We developed a transport-coupled kinetic model that captures these spectroscopic observations and provides insight into the processes controlling interfacial concentrations of reactants and intermediates, aiding future efforts toward tailoring reaction microenvironments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Perspective on Multiscale Modeling of Explicit Solvation-Enabled Simulations of Catalysis at Liquid–Solid Interfaces

Catalysis at liquid-solid interfaces is profoundly influenced by the interfacial solvent structure, which affects catalytic activity, selectivity, and reaction pathways. This perspective discusses state-of-the-art multiscale modeling methods that integrate quantum mechanics and molecular mechanics approaches to apply explicit solvent molecules to capture these interfacial phenomena. Specifically, the construction of multiscale models, the importance of capturing the interfacial solvent structure, and the computational strategies used to achieve this are explored, and the challenges in balancing chemical accuracy with computational expense are highlighted. Additionally, this perspective addresses the limitations of current methods. Opportunities for integrating machine learning are proposed. Here, by advancing the efficiency and user friendliness of multiscale modeling, it is argued that deeper insights into heterogeneous catalysis in liquid phases can be provided, which will ultimately contribute to the development of more efficient catalytic processes.

Ab initio molecular dynamics↗

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗