Shock waves in the dissipative Toda lattice

We consider the propagation of a shock wave (SW) in the damped Toda lattice. The SW is a moving boundary between two semi-infinite lattice domains with different densities. A steadily moving SW may exist if the damping in the lattice is represented by an ``inner'' friction, which is a discrete analog of the second viscosity in hydrodynamics. The problem can be considered analytically in the continuum approximation, and the analysis produces an explicit relation between the SW's velocity and the densities of the two phases. Numerical simulations of the lattice equations of motion demonstrate that a stable SW establishes if the initial velocity is directed towards the less dense phase; in the opposite case, the wave gradually spreads out. The numerically found equilibrium velocity of the SW turns out to be in a very good agreement with the analytical formula even in a strongly discrete case. If the initial velocity is essentially different from the one determined by the densities (but has the correct sign), the velocity does not significantly alter, but instead the SW adjusts itself to the given velocity by sending another SW in the opposite direction.Comment: 10 pages in LaTeX, 5 figures available upon regues

Collective Effects in Settling of Spheroids under Steady-State Sedimentation

We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.Peer reviewe

Sedimentation dynamics of spherical particles in confined geometries

We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing Lx. By systematically varying Lx we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of Lx. We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to Lx. We also find that the behavior of the corresponding diffusion coefficients as a function of Lx is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.Peer reviewe

3D Dose-Driven, Automatic VMAT Machine Parameter Generation with Deep Learning

Purpose/Objective(s): Recent research efforts utilizing knowledge-based treatment planning for the prediction of 3D radiation dose distributions from planning structure sets have achieved positive results. Most ongoing efforts to generate deliverable plans from the predicted doses rely on full inverse optimizations using dose-volume histogram (DVH) objectives derived from these doses. In this study, we aim to leverage deep learning (DL) to rapidly generate machine delivery parameters for volumetric modulated arc therapy (VMAT) from predicted desired doses. Materials/Methods: Data of 50 previously treated patients at our institution with prostate adenocarcinoma who received definitive radiotherapy were retrospectively obtained. All plans were generated with a one-arc VMAT technique, with conventional fractionation (78 Gy in 39 fx or 79.2 Gy in 44 fx to the prostate gland +/- seminal vesicles). A multi-task U-Net was constructed: it takes the 2D projections of the 3D dose and planning structures as inputs, and it predicts the numerical multi-leaf collimator (MLC) sequence and weights for the 178 control points. Five cases were randomly selected for testing only, and the remaining 45 formed the training set. The algorithm was implemented in Python 3.8 with PyTorch 1.7 as the DL framework. Model training was performed on a GPU. The DL-predicted plans underwent further inverse optimization with the 3D-dose-derived DVH objectives, utilizing only the last step of the Photon Optimizer (PO) in a treatment planning system. The optimization time and plan quality were compared to plans generated with one full PO optimization with the same objectives and clinical plans (all normalized to D95%=100% Rx dose). Results: The DL model was trained for 200 epochs. On average, DL-predicted plans could be optimized in 22% (range, 18-26%) of the time required for full optimization plans. Dosimetric comparison (Table 1) demonstrated that the quality of the DL-predicted plans was comparable with clinical plans and full optimization plans, but the DL-predicted plans tended to have increased dose inhomogeneity within the PTVs. Conclusion: We demonstrated the feasibility of rapidly generating deliverable VMAT plans from desired 3D doses with deep learning. Further work is needed to improve PTV dose homogeneity and generalize the method to multi-arc VMAT delivery

Regeneration of Stochastic Processes: An Inverse Method

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.Comment: 5 pages, two columns, 7 figs. to appear, The European Physical Journal B (2006