We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modell…
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48 results for “confined polymers”
The study examines knot probabilities in confined lattice polygons.
problem Determining the relative knotting probabilities in confined lattice knots.
method Used Monte Carlo algorithms to enumerate conformations of lattice knots in a confined volume.
result Relative knotting probabilities are small, with the model dominated by unknots.
Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. W…
Study on entanglement complexity of confined ring polymers in lattice tubes.
problem Understanding the entanglement complexity of confined ring polymers in lattice tubes.
method Applied knot theory to extend and prove results about the complexity of 2SAPs.
result Proved that all but exponentially few size m 2SAPs have F complexity that grows at least linearly in m as m approaches infinity.
Proposes a new model to predict polymer properties by integrating various data types.
problem Inaccurate polymer property prediction due to separate modeling of different data types.
method Multi-modal cascade feature transfer using GCN for chemical structure and molecular descriptors.
result Empirically evaluated model shows higher predictive performance than single-feature approaches.
Improved prediction of polymer morphology through machine learning and simulations.
problem Understanding and predicting the morphology of multi-component polymer blends.
method Modified Cahn-Hilliard model for simulations, machine learning for clustering and prediction.
result Machine learning achieved 90% accuracy in predicting polymer morphology.
Inverse design is an outstanding challenge in disordered systems with multiple length scales such as polymers, particularly when designing polymers with desired phase behavior. We demonstrate high-accuracy tuning of poly(2-oxazoline) cloud point via machine learning. With a design space of four repeating units and a ra…
In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of in a cube, the mean sum of squared linking numbers and the mean sum of square…
The space writhes and signatures of polymer knotscond-mat.soft
Study shows space writhe closely correlates with knot signature in polymers.
problem Understanding the relationship between space writhe and knot signatures in knotted polymers.
method Performed Langevin dynamics simulations of knotted polymers to measure space writhe.
result Space writhe is strongly correlated with knot signature in complex knots.
Bayesian modeling predicts hydroxide ion conductivity in polymer membranes.
problem Quantitative relationship between hydrophilic domain size and hydroxide ion conductivity in polymer membranes is unknown.
method Bayesian sparse modeling applied to copolymer composition data.
result Composition-derived features are identified as critical for predicting hydroxide ion conductivity.
Topologically Directed Simulations Reveal the Impact of Geometric Constraints on Knotted Proteinsmath.GT
Method optimizes knotting pathways in constrained polymers.
problem Understanding how geometric constraints affect knot formation in polymers.
method Topological steering using knotoid spectrum and mean unravelling number.
result Geometric constraints increase the frequency of twist knots in polymers.
A novel symmetry in nanocarbons: pre-constant discrete principal curvature structurecond-mat.mtrl-sci
Novel symmetry found in nanocarbons' discrete principal curvature structure.
problem Identifying novel symmetries in nanocarbons' geometric structures.
method First-principles calculations and discrete geometry analysis.
result Discovery of a novel symmetry (pre-constant discrete principal curvature) in nanocarbons.
Aggregation and structural phase transitions of semiflexible polymer bundles: a braided circuit topology approachcond-mat.soft
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
HAL accelerates the generation of training sets for accurate interatomic potentials.
problem Generating accurate and transferable interatomic potentials is time-consuming and requires expert input.
method HAL framework using a physically motivated sampler with a biasing term to drive high uncertainty configurations.
result HAL-generated training databases for alloys and polymers predict macroscopic properties with high accuracy.
Machine learning classifies polymer links with high accuracy.
problem Classifying knots and links in polymer melts and biological systems.
method Feedforward neural network trained on writhe density matrix.
result 97% accuracy in classifying six prime links across temperatures and lengths.
The discovery of processes for the synthesis of new materials involves many decisions about process design, operation, and material properties. Experimentation is crucial but as complexity increases, exploration of variables can become impractical using traditional combinatorial approaches. We describe an iterative met…
Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.
problem Understanding the growth rate of confined subgroups in groups with contracting elements.
method Through boundary actions, analyzing the Hopf decomposition and quotient growth.
result Confined subgroups have a growth rate strictly greater than half of the ambient growth rate.
Fast algorithm samples confined polygons efficiently.
problem Sampling confined random equilateral closed polygons efficiently.
method Uses symplectic geometry to sample moment polytope, leading to a linear-time algorithm.
result Explicit formulas for expected distances and total curvature of vertices to the origin.
We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking …
Enhances graph neural networks by creating virtual data examples.
problem Lack of examples to identify optimal graph rationales in graph applications.
method Introduces environment replacement to create virtual data examples and proposes a framework for rationale-environment separation and representation learning.
result Demonstrates the effectiveness and efficiency of the augmentation-based graph rationalization framework on molecular and polymer datasets.
CONFINE enhances neural networks' interpretability without sacrificing accuracy.
problem Lack of interpretability in deep neural networks, especially in healthcare.
method CONFINE uses conformal prediction to generate prediction sets with robust uncertainty estimates.
result CONFINE achieves correct efficiency up to 3.3% higher than original accuracy.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
New framework shows -simplicity for groups without certain subalgebras.
problem Characterizing -simplicity of groups.
method Introducing confined subalgebras and Uniformly Recurrent States.
result A countable discrete group is -simple if it has no non-trivial amenable confined subalgebras.
Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.
problem Describing hyperbolic actions of solvable groups with higher rank abelianizations.
method Extends confining subset theory to apply to solvable groups with higher rank abelianizations.
result Complete description of hyperbolic actions of generalized solvable Baumslag-Solitar groups.
Paper introduces simplified formulas for Milnor's triple linking number.
problem Computational difficulty in calculating Jones polynomial for topological polymers.
method Developed Gauss diagram formulas for Milnor's Vassiliev invariants.
result Introduced non-torsion valued Milnor's triple linking number.
Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curva…
Sharp growth tightness proven for group quotients.
problem Growth behavior of group quotients by confined subgroups.
method Statistically convex-cocompact action with contracting elements.
result Sharp growth tightness proven, with applications to uniformly recurrent subgroups.
Study on membranes under confinement, proving existence and regularity of minimizers.
problem Existence and regularity of minimizers for constrained Helfrich energy.
method Elliptic system analysis, careful study of measure-valued Lagrange multiplier.
result Optimal regularity for solutions throughout branch points, rigid behavior for unit ball minimizers.
Minimal submanifolds confined in space are highly restricted.
problem Understanding minimal submanifolds in confined spaces.
method Analyzing structural restrictions and volume growth properties.
result Proper minimal immersions with sublinear height growth must have Euclidean volume growth.
New methods assess topological entanglement in periodic systems.
problem Assessing topological entanglement in systems with periodic boundary conditions.
method Introducing Periodic Jones polynomial and Cell Jones polynomial.
result Periodic Jones polynomial is a recurring factor of Jones polynomial of finite cutoffs.
Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
problem Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
method Identifying entropic barriers arising from the interplay between curvature variations along low-loss paths and noise in optimization dynamics.
result Curvature-induced entropic forces bias noisy dynamics back toward the endpoints, explaining the confinement and connectivity of solutions.
Concepts of polymer statistical topologycond-mat.stat-mech
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called…
We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set . We prove existence, regularity and some structural properties of minimizers. In particular, when is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a…
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of…
Study of bound states in quantum layers with confining potentials.
problem Investigating bound states in quantum layers with confining potentials.
method Developed a general approach using parallel coordinates based on the surface but outside its cut locus.
result Discrete eigenvalues exist for certain quantum layers with positive total Gauss curvature.
Classifies quantum particle behavior on a special cylinder.
problem Quantum confinement and transmission on a Grushin cylinder.
method Characterizes self-adjoint realizations of the Laplace-Beltrami operator.
result Identifies physically meaningful extensions of the Hamiltonian.
Hydrogen atom confined inside an inverted-Gaussian potentialphysics.atom-ph
Hydrogen atom confined in an inverted-Gaussian potential, with detailed numerical methods and results.
problem Studying hydrogen atom in a specific potential.
method Three numerical methods: Lagrange-mesh, fourth order finite differences, and finite element method.
result Accurate numerical results for hydrogen atom energies and eigenfunctions, improving previous literature.
Prediction of flow and elastic stresses in a viscoelastic turbulent channel flow using convolutional neural networksphysics.flu-dyn
Neural networks predict flow and elastic stresses in viscoelastic turbulence.
problem Predicting flow and elastic stresses in viscoelastic turbulent flows using limited experimental data.
method Convolutional neural networks trained on wall-normal velocity and pressure data.
result Neural networks accurately predict flow and elastic stresses, especially during low-drag events.
New model generates larger molecules more effectively.
problem Previous graph generation techniques struggle with larger molecules.
method Hierarchical graph encoder-decoder using structural motifs.
result Model significantly outperforms previous baselines on molecule generation tasks.
Geometric QCD framework establishes stable vacuum for quark confinement.
problem Quark confinement in QCD.
method Geometric construction of stable vacuum using Hodge-dual surfaces.
result Existence and stability of the Hodge-dual surface in 4D ensures quark confinement.
Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylindersmath.DG
The study characterizes hypersurfaces in weighted cylinders and generalizes confinement properties.
problem Characterizing hypersurfaces in weighted Riemannian products.
method Analyzing parabolic hypersurfaces with boundary in weighted cylinders.
result Generalized confinement properties of hypersurfaces in weighted cylinders.
Random knotting in very long off-lattice self-avoiding polygonscond-mat.stat-mech
Study on knotting in very long polymer chains, finding Poisson distribution for prime knot types.
problem Understanding knotting in very long polymer chains.
method Generated and analyzed polygons of size using tree data structure and pivot algorithm. Used new knot diagram simplification and invariant-free classification.
result Number of prime summands of knot type in a random -gon is well described by a Poisson distribution.
Exploring Generative Physics Models with Scientific Priors in Inertial Confinement Fusionphysics.comp-ph
There is significant interest in using modern neural networks for scientific applications due to their effectiveness in modeling highly complex, non-linear problems in a data-driven fashion. However, a common challenge is to verify the scientific plausibility or validity of outputs predicted by a neural network. This w…
A machine learning model captures non-Newtonian fluid dynamics from molecular details.
problem Creating accurate non-Newtonian fluid models from molecular data.
method Developed a machine learning framework that maps micro-scale polymer configurations to macro-scale fluid dynamics, preserving molecular fidelity.
result The deep non-Newtonian model (DeePN) accurately predicts fluid behavior without empirical closures.
We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold equipped with a smooth measure , possibly degenerate or singular near the metric boundary of , and in presence of a real-valued potential . The main …
Improved neural network surrogates for ICF using manifold and cycle consistency.
problem Modeling and predicting complex physical processes in inertial confinement fusion.
method Training neural network surrogates that are consistent with the physical manifold and cyclically consistent.
result Surrogates are superior in predictive performance, more resilient to sampling artifacts, and more data efficient.
Proof of Knot Entropy Conjecture for tube lattice polygons.
problem Proving exponential growth rate of knot polygons equals unknot polygons.
method Upper and lower bounds on polygon counts, braid insertions, and pattern theorems.
result Established the Knot Entropy Conjecture for tube lattice polygons.
We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of vi…