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1. A generalized Rayleigh-Plesset equation for ions with solvent fluctuations

   Fan, C.; Li, B.; White, M. (June 2021, SIAM journal on applied mathematics)

   null (Ed.)

   We introduce a mathematical modeling framework for the conformational dynamics of charged molecules (i.e., solutes) in an aqueous solvent (i.e., water or salted water). The solvent is treated as an incompressible fluid, and its fluctuating motion is described by the Stokes equation with the Landau–Lifschitz stochastic stress. The motion of the solute-solvent interface (i.e., the dielectric boundary) is determined by the fluid velocity together with the balance of the viscous force,hydrostatic pressure, surface tension, solute-solvent van der Waals interaction force, and electrostatic force. The electrostatic interactions are described by the dielectric Poisson–Boltzmann theory.Within such a framework, we derive a generalized Rayleigh–Plesset equation, a nonlinear stochastic ordinary differential equation (SODE), for the radius of a spherical charged molecule, such as anion. The spherical average of the stochastic stress leads to a multiplicative noise. We design and test numerical methods for solving the SODE and use the equation, together with explicit solvent molecular dynamics simulations, to study the effective radius of a single ion. Potentially, our general modeling framework can be used to efficiently determine the solute-solvent interfacial structures and predict the free energies of more complex molecular systems. 

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2. Preparation of Macroscopic Block‐Copolymer‐Based Gyroidal Mesoscale Single Crystals by Solvent Evaporation

   https://doi.org/10.1002/adma.201902565  

   Susca, Ethan_M; Beaucage, Peter_A; Thedford, R_Paxton; Singer, Andrej; Gruner, Sol_M; Estroff, Lara_A; Wiesner, Ulrich (August 2019, Advanced Materials)

   Abstract Properties arising from ordered periodic mesostructures are often obscured by small, randomly oriented domains and grain boundaries. Bulk macroscopic single crystals with mesoscale periodicity are needed to establish fundamental structure–property correlations for materials ordered at this length scale (10–100 nm). A solvent‐evaporation‐induced crystallization method providing access to large (millimeter to centimeter) single‐crystal mesostructures, specifically bicontinuous gyroids, in thick films (>100 µm) derived from block copolymers is reported. After in‐depth crystallographic characterization of single‐crystal block copolymer–preceramic nanocomposite films, the structures are converted into mesoporous ceramic monoliths, with retention of mesoscale crystallinity. When fractured, these monoliths display single‐crystal‐like cleavage along mesoscale facets. The method can prepare macroscopic bulk single crystals with other block copolymer systems, suggesting that the method is broadly applicable to block copolymer materials assembled by solvent evaporation. It is expected that such bulk single crystals will enable fundamental understanding and control of emergent mesostructure‐based properties in block‐copolymer‐directed metal, semiconductor, and superconductor materials. 

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3. Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation

   Yan, Keqiang; Li, Xiner; Ling, Hongyi; Ashen, Kenna; Edwards, Carl; Arróyave, Raymundo; Zitnik, Marinka; Ji, Heng; Qian, Xiaofeng; Qian, Xiaoning; et al (December 2024, 38th Conference on Neural Information Processing Systems (NeurIPS 2024).)

   Globerson, A; Mackey, L; Belgrave, D; Fan, A; Paquet, U; Tomczak, J; Zhang, C (Ed.)

   We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods. 

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4. Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation

   Yan, Keqiang; Li, Xiner; Ling, Hongyi; Ashen, Kenna; Edwards, Carl; Arróyave, Raymundo; Zitnik, Marinka; Ji, Heng; Qian, Xiaofeng; Qian, Xiaoning; et al (December 2024, ArXiv)

   We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods. 

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5. An Integral Equation Model for PET Imaging

   Tang, Xinhuang; Schmidtlein, Charles Ross; Li, Si; Xu, Yuesheng (January 2021, International journal of numerical analysis and modeling)

   Positron emission tomography (PET) is traditionally modeled as discrete systems. Such models may be viewed as piecewise constant approximations of the underlying continuous model for the physical processes and geometry of the PET imaging. Due to the low accuracy of piecewise constant approximations, discrete models introduce an irreducible modeling error which fundamentally limits the quality of reconstructed images. To address this bottleneck, we propose an integral equation model for the PET imaging based on the physical and geometrical considerations, which describes accurately the true coincidences. We show that the proposed integral equation model is equivalent to the existing idealized model in terms of line integrals which is accurate but not suitable for numerical approximation. The proposed model allows us to discretize it using higher accuracy approximation methods. In particular, we discretize the integral equation by using the collocation principle with piecewise linear polynomials. The discretization leads to new ill-conditioned discrete systems for the PET reconstruction, which are further regularized by a novel wavelet-based regularizer. The resulting non-smooth optimization problem is then solved by a preconditioned proximity fixed-point algorithm. Convergence of the algorithm is established for a range of parameters involved in the algorithm. The proposed integral equation model combined with the discretization, regularization, and optimization algorithm provides a new PET image reconstruction method. Numerical results reveal that the proposed model substantially outperforms the conventional discrete model in terms of the consistency to simulated projection data and reconstructed image quality. This indicates that the proposed integral equation model with appropriate discretization and regularizer can significantly reduce modeling errors and suppress noise, which leads to improved image quality and projection data estimation. 

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