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At least 217 records · Page 12

Computation of shear viscosity of colloidal suspensions by SRD-MD

The behaviour of sheared colloidal suspensions with full hydrodynamic interactions (HIs) is numerically studied. To this end, we use the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) method. The shear viscosity of colloidal suspensions is computed for different volume fractions, both for dilute and concentrated cases. We verify that HIs help in the collisions and the streaming of colloidal particles, thereby increasing the overall shear viscosity of the suspension. Our results show a good agreement with known experimental, theoretical, and numerical studies. This work demonstrates the ability of SRD-MD to successfully simulate transport coefficients that require correct modelling of HIs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Continuation of probability density functions using a generalized Lyapunov approach

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also the stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Critical analysis and remedy of switching failures in straintronic logic using Bennett clocking in the presence of thermal fluctuations

Straintronic logic is a promising platform for beyond Moore's law computing. Using Bennett clocking mechanism, information can propagate through an array of strain-mediated multiferroic nanomagnets, exploiting the dipolar coupling between the magnets without having to physically interconnect them. Here, we perform a critical analysis of switching failures, i.e., error in information propagation due to thermal fluctuations through a chain of such straintronic devices. We solved stochastic Landau-Lifshitz-Gilbert equation considering room-temperature thermal perturbations and show that magnetization switching may fail due to inherent magnetization dynamics accompanied by thermally broadened switching delay distribution. Avenues available to circumvent such issue are proposed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effects of QCD equation of state on the stochastic gravitational wave background

Cosmological phase transitions can be a source of Stochastic Gravitational Wave (SGW) background. Apart from the dynamics of the phase transition, the characteristic frequency and the fractional energy density Ω{sub gw} of the SGW depends upon the temperature of the transition. In this article, we compute the SGW spectrum in the light of QCD equation of state provided by the lattice results. We find that the inclusion of trace anomaly from lattice QCD, enhances the SGW signal generated during QCD phase transition by ∼ 50% and the peak frequency of the QCD era SGW are shifted higher by ∼ 25% as compared to the earlier estimates without trace anomaly. This result is extremely significant for testing the phase transition dynamics near QCD epoch.

79 ASTRONOMY AND ASTROPHYSICS↗

The effect of non-uniform mass loading on the linear, temporal development of particle-laden shear layers

The effect of non-uniformity in bulk particle mass loading on the linear development of a particle-laden shear layer is analyzed by means of a stochastic Eulerian-Eulerian model. From the set of governing equations of the two-fluid model, a modified Rayleigh equation is derived that governs the linear growth of a spatially periodic disturbance. Eigenvalues for this Rayleigh equation are determined numerically using proper conditions at the co-flowing gas and particle interface locations. For the first time, it is shown that non-uniform loading of small-inertia particles (Stokes number (St) <0.2) may destabilize the inviscid mixing layer development as compared to the pure-gas flow. The destabilization is triggered by an energy transfer rate that globally flows from the particle phase to the gas phase. For intermediate St (1 < St < 10), a maximum stabilizing effect is computed, while at larger St, two unstable modes may coexist. The growth rate computations from linear stability analysis are verified numerically through simulations based on an Eulerian-Lagrangian (EL) model based on the inviscid Euler equations and a point particle model. The growth rates found in numerical experiments using the EL method are in very good agreement with growth rates from the linear stability analysis and validate the destabilizing effect induced by the presence of particles with low St.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A probabilistic graphical model based stochastic input model construction

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A simplified model for dynamics of cell rolling and cell-surface adhesion

We propose a three dimensional model for the adhesion and rolling of biological cells on surfaces. We study cells moving in shear flow above a wall to which they can adhere via specific receptor-ligand bonds based on receptors from selectin as well as integrin family. The computational fluid dynamics are governed by the lattice-Boltzmann method. The movement and the deformation of the cells is described by the immersed boundary method. Both methods are fully coupled by implementing a two-way fluid-structure interaction. The adhesion mechanism is modelled by adhesive bonds including stochastic rules for their creation and rupture. We explore a simplified model with dissociation rate independent of the length of the bonds. We demonstrate that this model is able to resemble the mesoscopic properties, such as velocity of rolling cells.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Biomanufacturing and self-propulsion dynamics of nanoscale bacteria-enabled autonomous delivery systems

Flagellated bacteria have superb self-propulsion capabilities and are able to effectively move through highly viscous fluid and semi-solid (porous) environments. This innate aptitude has been harvested for whole-cell actuation of bio-hybrid microrobotic systems with applications in directed transport and microassembly. In this work, we present the biomanufacturing of Nanoscale Bacteria-Enabled Autonomous Delivery Systems (NanoBEADS) by controlled self-assembly and investigate the role of nanoparticle load on the dynamics of their self-propulsion in aqueous environments. Each NanoBEADS agent is comprised of spherical polystyrene nanoparticles assembled onto the body of a flagellated Escherichia coli bacterium. We demonstrate that the NanoBEADS assembly configuration is strongly dependent upon the nanoparticles to bacteria ratio. Furthermore, we characterized the stochastic motion of the NanoBEADS as a function of the quantity and size of the nanoparticle load and computationally analyzed the effect of the nanoparticle load on the experienced drag force. We report that the average NanoBEADS swimming speed is reduced to 65% of the free-swimming bacteria speed (31 μm/s) at the highest possible load. NanoBEADS can be utilized as single agents or in a collaborative swarm in order to carry out specific tasks in a wide range of applications ranging from drug delivery to whole cell biosensing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Time series, correlation matrices and random matrix models

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.

97 MATHEMATICS AND COMPUTING↗

On the numerical treatment of dissipative particle dynamics and related systems

We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods considered includes dissipative particle dynamics (DPD) as well as extended stochastic-dynamics models incorporating a generalized pairwise thermostat scheme in which stochastic forces are eliminated and the coefficient of dissipation is treated as an additional auxiliary variable subject to a feedback (kinetic energy) control mechanism. In the latter case, we consider the addition of a coupling of the auxiliary variable, as in the Nosé–Hoover–Langevin (NHL) method, with stochastic dynamics to ensure ergodicity, and find that the convergence of ensemble averages is substantially improved. To this end, splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. In terms of computational efficiency as measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the pairwise NHL method compared to popular alternative schemes (up to an 80% improvement), without degradation of convergence rate. The momentum-conserving thermostat technique described here provides a consistent hydrodynamic model in the low-friction regime, but it will also be of use in both equilibrium and nonequilibrium molecular simulation applications owing to its efficiency and simple numerical implementation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The relationship between anatomic noise and volumetric breast density for digital mammography

Purpose: The appearance of parenchymal/stromal patterns in mammography have been characterized as having a Wiener power spectrum with an inverse power-law shape described by the exponential parameter, {beta}. The amount of fibroglandular tissue, which can be quantified in terms of volumetric breast density (VBD), influences the texture and appearance of the patterns formed in a mammogram. Here, a large study is performed to investigate the variations in {beta} in a clinical population and to indicate the relationship between {beta} and breast density. Methods: From a set of 2686 cranio-caudal normal screening mammograms, the parameter {beta} was extracted from log-log fits to the Wiener spectrum over the range 0.15-1 mm{sup -1}. The Wiener spectrum was calculated from regions of interest in the compression paddle contact region of the breast. An in-house computer program, Cumulus V, was used to extract the volumetric breast density and identify the compression paddle contact regions of the breast. The Wiener spectra were calculated with and without modulation transfer function (MTF) correction to determine the impact of VBD on the intrinsic anatomic noise. Results: The mean volumetric breast density was 25.5% ({+-}12.6%) over all images. The mean {beta} following a MTF correction which decreased the {beta} slightly ( Almost-Equal-To -0.08) was found to be 2.87. Varying the maximum of the spatial frequency range of the fits from 0.7 to 1.0, 1.25 or 1.5 mm{sup -1} showing small decreases in the result, although the effect of the quantum noise power component on reducing {beta} was clearly observed at 1.5 mm{sup -1}. Conclusions: The texture parameter, {beta}, was found to increase with VBD at low volumetric breast densities with an apparent leveling off at higher densities. The relationship between {beta} and VBD measured here can be used to create probabilistic models for computer simulations of detectability. As breast density is a known risk predictor for breast cancer, the correlation between {beta} and VBD suggests that {beta} may provide predictive information and this will be investigated in the future.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for 1/f noise in solid-state quantum information processors. Here we present an approach for simulating Hamiltonian classical stochastic noise that performs temporal coarse-graining by effectively integrating out the high-frequency components of the noise. We focus on the case where the stochastic noise can be expressed as a sum of Ornstein-Uhlenbeck processes. Temporal coarse-graining is then achieved by conditioning the stochastic process on a coarse realization of the noise, expressing the conditioned stochastic process in terms of a sum of smooth, deterministic functions and bridge processes with boundaries fixed at zero, and performing the ensemble average over the bridge processes. For Ornstein-Uhlenbeck processes, the deterministic components capture all dependence on the coarse realization, and the stochastic bridge processes are not only independent but taken from the same distribution with correlators that can be expressed analytically, allowing the associated noise propagators to be precomputed once for all simulations. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages, such as a simple concatenation rule, that we highlight with numerical examples.

Albash, Tameem [Sandia National Lab. (SNL-NM), Alb↗

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

Energy transport by eddies is diagnosed from a series of simulations of stochastically forced, inhomogeneous two-dimensional turbulence—barotropic dynamics on the f-plane. The divergence of the energy flux is compared to diffusive models, both fractional and harmonic, and the inferred diffusivity κ is compared to a mixing-length model κ ∝ Vℓ where V and ℓ are eddy velocity and length scales, respectively. The flux-divergence is found to be well approximated by Laplacian diffusion with a mixing-length approximation. This study provides some support for diffusive modeling of mesoscale eddy energy transport in ocean model parameterizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗