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Coarse-graining conformational dynamics with multi-dimensional generalized Langevin equation: how, when, and why

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arXiv 2024年

作者： Xie, Pinchen Qiu, Yunrui Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry University of Wisconsin-Madison MadisonWI53706 United States AI for Science Institute Beijing100080 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100084 China

A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained conformational dynamics. Constrained by the fluctuation-dissipation theorem, the approach can build coarse-grained models in dynamical consistency with all-atom molecular dynamics. We also propose practical criteria for AIGLE to enforce long-term dynamical consistency. Case studies of a toy polymer, with 20 coarse-grained sites, and the alanine dipeptide, with two dihedral angles, elucidate why one should adopt AIGLE or its Markovian limit for modeling coarse-grained conformational dynamics in practice. © 2024, CC BY.

关键词： Coarse-grained modeling

Gap sensitivity reveals universal behaviors in optimized photonic crystal and disordered networks

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arXiv 2021年

作者： Klatt, Michael Andreas Steinhardt, Paul J. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Institut für Theoretische Physik University of Erlangen-Nürnberg Staudtstr. 7 Erlangen91058 Germany Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α) ≡ d∆(α)/dα, the first derivative of the optimal gap-to-midgap ratio ∆(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a one-dimensional quarter-wave stack, SQWS(α). Even more surprisingly, the values of S(α) for our disordered networks converge to SQWS(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic *** Codes 78A48, 78M50 (Primary) 82D25, 82D30, 52C99 (Secondary) © 2021, CC BY-SA.

关键词： Photonic band gap

Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales

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Physical Review X 2023年第1期13卷 011038-011038页

作者： Oliver H. E. Philcox Salvatore Torquato Department of Astrophysical Sciences Princeton University Princeton New Jersey 08540 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Center for Theoretical Physics Department of Physics Columbia University New York New York 10027 USA Simons Foundation New York New York 10010 USA Department of Chemistry Department of Physics Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much l

关键词： Large scale structure of the Universe

Optimized large hyperuniform binary colloidal suspensions in two dimensions

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arXiv 2020年

作者： Ma, Zheng Lomba, Enrique Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Instituto de Química Física Rocasolano CSIC Calle Serrano 119 MadridE-28006 Spain Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The creation of disordered hyperuniform materials with potentially extraordinary optical properties requires a capacity to synthesize large samples that are effectively hyperuniform down to the nanoscale. Motivated by this challenge, we propose a fabrication protocol using binary paramagnetic colloidal particles confined in a 2D plane. The strong and long-ranged dipolar interaction induced by a tunable magnetic field is free from screening effects that attenuates long-ranged electrostatic interactions in charged colloidal systems. Specifically, we find a family of optimal size ratios that makes the two-phase system effectively hyperuniform. We show that hyperuniformity is a general consequence of low isothermal compressibilities, which makes our protocol suitable to systems with other long-ranged soft interactions, dimensionalities and/or polydispersity. Our methodology paves the way to synthesize large photonic hyperuniform materials that function in the visible to infrared range and hence may accelerate the discovery of novel photonic materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Suspensions (fluids)

Flagellum Pumping Efficiency in Shear-Thinning Viscoelastic Fluids

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arXiv 2023年

作者： Barrett, Aaron Fogelson, Aaron L. Gregory Forest, M. Gruninger, Cole Lim, Sookkyung Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Department of Mathematical Sciences University of Cincinnati CincinnatiOH United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment. Copyright © 2023, The Authors. All rights reserved.

关键词： Shear thinning

Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

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Physical Review B 2022年第6期105卷 064204-064204页

作者： F. Sgrignuoli S. Torquato L. Dal Negro Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary's Street Boston Massachusetts 02215 USA Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA Division of Material Science and Engineering Boston University 15 Saint Mary's Street Brookline Massachusetts 02446 USA Department of Physics Boston University 590 Commonwealth Avenue Boston Massachusetts 02215 USA

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed subradiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

关键词： Anderson localization Light-matter interaction Mesoscopics Photonics Scattering theory Weak localization Metamaterials

ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

In situ characterization of nanoparticles using rayleigh scattering

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arXiv 2017年

作者： Santra, Biswajit Shneider, Mikhail N. Car, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Mechanical and Aerospace Engineering Department Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the Rayleigh scattering probe is adequate to detect nanoparticles as small as C60 at the expected concentrations of synthesis conditions in the arc periphery. Larger asymmetric nanoparticles would yield brighter signals, making possible to follow the evolution of the growing nanoparticle population from the evolution of the scattered intensity. Observable spectral features include characteristic resonant behaviour, shape-dependent depolarization ratio, and mass-dependent line shape. Direct observation of nanoparticles in the early stages of growth with unobtrusive laser probes should give insight on the particle formation mechanisms and may lead to better-controlled synthesis protocols. Copyright © 2017, The Authors. All rights reserved.

关键词： Rayleigh scattering

A Nodal Immersed Finite Element-Finite Difference Method

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SSRN

SSRN 2022年

作者： Wells, David Vadala-Roth, Ben Lee, Jae Ho Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States U.S. Army Corps of Engineers Engineer Research and Development Center Coastal and Hydraulic Laboratory VicksburgMS United States Department of Mechanical Engineering Institute for Computational Medicine Johns Hopkins University BaltimoreMD United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses and forces on a structural mesh and a finite difference (FD) method to approximate the momentum of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to

关键词： Fluid structure interaction