Classifies soap film surfaces with vertical potentials.
problem Classifying soap film surfaces with vertical potentials.
method Variational characterization of -elastic curves.
result Obtains a full description of -elastic curves.
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48 results for “potential energy surfaces”
We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. we notably exhibit a new residue which quantifies the potential loss of energy in collar regions. Thanks to these residues, we also prove compactness of Wil…
Study predicts wind energy potential in Gulf of Oman using climate models.
problem Predicting future wind energy potential in the Gulf of Oman.
method Used ERA5 and MENA simulations to project historical and future wind energy variability.
result Selected locations have suitable potential for wind power turbine construction.
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this a…
Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentialsphysics.comp-ph
New method uses geometric moments for accurate machine learning potentials.
problem Creating high-dimensional potential energy surfaces efficiently.
method Feed-forward neural networks with invariant local molecular descriptors based on geometric moments.
result Accuracy comparable to established models, high efficiency.
We derive global estimates in critical scale invariant norms for solutions of elliptic systems with antisymmetric potentials and almost holomorphic Hopf differential in two dimensions. Moreover we obtain new energy identities in such norms for sequences of solutions of these systems. The results apply to harmonic maps …
Study fractional Allen-Cahn equation and nonlocal minimal surfaces, improving energy and perimeter estimates.
problem Properties of solutions to fractional Allen-Cahn equation and stationary nonlocal minimal surfaces.
method Quantitative stratification principle applied to fractional Allen-Cahn equation, leading to optimal estimates.
result Sharp potential energy and perimeter estimates for fractional Allen-Cahn equation and nonlocal minimal surfaces.
Study on the Euler-Plateau energy with elastic modulus, focusing on minimizers and critical surfaces.
problem Minimizing the Euler-Plateau energy with elastic modulus.
method Analyzing the energy functional and its minimizers, considering different boundary conditions and topological constraints.
result Potential minimizers are highly dependent on physical rigidity parameters, and the area of critical surfaces can be computed from boundary data.
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimisers are convex in dimension two. This positively answers an old question of Almgren. We also prove convexity of minimisers when the volume co…
A2I Transformer: Permutation-equivariant attention network for pairwise and many-body interactions with minimal featurizationphysics.comp-ph
A2I Transformer predicts atom energies from coordinates, avoiding heavy featurization.
problem Efficiently predicting atom energies from molecular coordinates with minimal featurization.
method End-to-end model using self-attention, permutation-equivariant.
result Stable predictions with significantly smaller errors than molecular dynamics simulations.
The paper studies minimal submanifolds with specific curvature properties in Euclidean space.
problem Minimal submanifolds with -umbilical properties in Euclidean space.
method Established a correspondence and developed a Weierstrass type method for local parametrization.
result Minimal, generic, -umbilic submanifolds are -rotational and have a parametric description.
The paper proves cylindrical nature of singular minimal ruled surfaces.
problem Understanding minimal potential energy surfaces under gravitational forces.
method Analyzing singular minimal ruled surfaces in Euclidean and Lorentz-Minkowski 3-spaces.
result Singular minimal ruled surfaces are cylindrical, including as α-catenary cylinders.
Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Groundphysics.chem-ph
Highly accurate potential energy surfaces are of key interest for the detailed understanding and predictive modeling of chemical systems. In recent years, several new types of force fields, which are based on machine learning algorithms and fitted to ab initio reference calculations, have been introduced to meet this r…
Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…
We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian potential and the initial Calabi energy is bounded by some constant. This is an extension of our previous work. We use the toric condition in a …
The Many-Body Expansion Combined with Neural Networksphysics.chem-ph
Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of fragments required for chemical accuracy is still prohibitively expensive for ab-initio MBE to compete with force fi…
Cormorant: Covariant Molecular Neural Networksphysics.comp-ph
We propose Cormorant, a rotationally covariant neural network architecture for learning the behavior and properties of complex many-body physical systems. We apply these networks to molecular systems with two goals: learning atomic potential energy surfaces for use in Molecular Dynamics simulations, and learning ground…
The paper constructs families of high genus CMC surfaces in the 3-sphere.
problem Existence and construction of high genus constant mean curvature surfaces.
method Implicit function theorem and iterative algorithm to compute power series expansions.
result Construction of complete and smooth families of CMC surfaces with increasing Willmore energy.
Minimizing the free energymath.AP
Sharp stability in Almgren problem solved in any dimension.
problem Quantitative stability in the radial isotropic Almgren problem.
method Developed a theory for estimating the sharp modulus under minimal assumptions.
result Sharp in any dimension, solving the critical mass problem.
Proposes linking energy and force uncertainty in deep learning potentials.
problem Uncertainty in predicted energies and forces in machine learning models.
method Introduces a spatially correlated noise process to link energy and force uncertainty.
result Demonstrates the approach on molecular datasets, linking energy and force uncertainties.
For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of smooth Calabi flow. We prove that the solution of combinatorial Calabi flow exists for all time. Moreover, the solution converges if and only if Thurston's circle packing exists. As a consequence, combinatorial Calabi flow pro…
The paper proposes a thermodynamic potential to guide training of generative models, breaking ergodicity to improve functionality.
problem Improving generative model functionality while limiting access to underrepresented patterns.
method Constructing a thermodynamic potential that guides training, leading to multiple minima in the free energy.
result Training a generative model breaks ergodicity, preventing escape into the high-temperature phase.
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by interpreting parametrized geodesics as the paths traced out in time by the motion of…
Multi-Fidelity Gaussian Process based Empirical Potential Development for Si:H Nanowiresphysics.comp-ph
Developed accurate empirical potentials for Si:H nanowires using multi-fidelity Gaussian process.
problem Accurate modeling of Si:H nanowires using fast but inaccurate empirical potentials and slow but accurate first-principle calculations.
method Employed multi-fidelity Gaussian process regression to integrate low-fidelity empirical potential data with high-fidelity first-principle calculations.
result Demonstrated the accuracy of developed empirical potentials for Si:H nanowires.
Stock mechanics: a general theory and method of energy conservation with applications on DJIAphysics.soc-ph
A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…
New formula connects Loewner energy to moving frames' renormalised energy.
problem Calculating Loewner energy of Jordan curves.
method Using renormalised energy of moving frames.
result Loewner energy as Kähler potential for Weil-Petersson space.
Paper finds relations between Willmore-type energies, weighted areas, and vertical potential energies for cylindrical critical points.
problem Tackles relations between three types of energy functions for cylindrical critical points.
method Uses differential equations and critical point analysis for Willmore-type energies and weighted areas.
result Generating curves coincide for Willmore-type energies and weighted areas, and similar results hold for Willmore-type energies and vertical potential energies.
Study shows inflation in 3+1D cosmologies with bounded scalar potential and specific symmetry.
problem Understanding inflation in 3+1D cosmologies with specific constraints.
method Mean curvature flow and asymptotic analysis of metric variations, stress-energy tensor, and inflaton field dynamics.
result Inflation occurs in 3+1D cosmologies with specific constraints, demonstrating it is possible with inhomogeneous initial conditions.
In this paper we consider a free boundary problem in the 3-dimensional Lorentz-Minkowski space which deals spacelike surfaces whose mean curvature is a linear function of the time coordinate and the boundary moves in a given support plane. We study spacelike surfaces that project one-to-one into a strip of the su…
In this paper we study some global properties of static potentials on asymptotically flat -manifolds in the nonvacuum setting. Heuristically, a static potential represents the (signed) length along of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…
Study classifies ruled surfaces critical to Dirichlet energy.
problem Identifying ruled surfaces critical to Dirichlet energy.
method Explicit parametrization of ruled surfaces.
result Classification of ruled surfaces as critical points of Dirichlet energy.
We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are co…
Study on infinite energy maps from surfaces to CAT(0) spaces.
problem Harmonic maps with infinite energy from Riemann surfaces to CAT(0) spaces.
method Estimates of energy growth near punctures, proof of uniqueness.
result Precise estimates of energy growth near punctures and proof of uniqueness of harmonic maps.
Energy quantization for surfaces with area, volume, and mean curvature constraints.
problem Energy quantization for constrained Willmore surfaces.
method Established through strong compactness under energy thresholds.
result Strong compactness of constrained Willmore surfaces, including minimizers.
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increas…
Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not …
Gradient flows for surface energies with tensor fields are derived and analyzed.
problem Deriving consistent gradient flows for surface energies involving tensor fields.
method Introducing different gauges of surface independence and demonstrating their effects on energy decrease.
result Consistent choice of gauge and time derivative is necessary for energy decrease.
The paper identifies magnetic ground states and their role in determining the conformal class of a surface.
problem Understanding the magnetic ground states and their relation to the conformal class of a surface.
method Analyzing the magnetic Laplacian and its eigenvalues on a Riemannian surface.
result The ground state spectrum uniquely determines the volume and conformal class of the metric.
Triangulates surfaces with bounded energy using diffeomorphisms.
problem Triangulating surfaces with bounded Kolasinski--Menger energy.
method Uses bounded distortion diffeomorphisms of subsets of a plane.
result Triangulation with bounded number of triangles.
New foliations found for critical surfaces of Hawking energy, resolving discrepancies.
problem Finding consistent critical surfaces for the Hawking energy in non-totally geodesic spacelike hypersurfaces.
method Constructing a unique local foliation of area constrained critical surfaces of the Hawking energy in the general case of non-totally geodesic spacelike hypersurfaces.
result Discrepancy found in the small sphere limit of the Hawking energy, explained and resolved.
Study finds surfaces in spherical caps that maximize modified energy.
problem Geometry of surfaces with free boundaries and capillary conditions.
method Monotonicity formulae and energy maximization analysis.
result Capillary minimal surfaces maximize a modified energy in their conformal orbit.
Bayesian optimization with Gaussian processes speeds up searches for stationary points.
problem Accelerating searches for stationary points on potential energy surfaces.
method Unified Bayesian optimization view using Gaussian process regression with derivative observations, inverse-distance kernels, and active learning.
result Surrogates can reduce the number of expensive electronic structure evaluations by an order of magnitude.
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternati…
Study on existence of ground states on curved spaces with conditions on potential growth.
problem Existence of ground states for aggregation-diffusion models on Cartan-Hadamard manifolds.
method Investigation of a free energy functional on Cartan-Hadamard manifolds, considering entropy and interaction energies.
result Necessary and sufficient conditions for existence of ground states are found, depending on the growth of the attractive potential.
Study bounds CMC surface index in 3-manifolds using energy.
problem Bounding the index of CMC surfaces in 3-manifolds.
method Energy comparison to prove linear upper bound.
result Linear upper bound on CMC surface index.
BESS shows potential in European markets for frequency support, but not for energy arbitrage.
problem Lack of profitability for BESS in energy arbitrage in most European markets.
method Proposed a general payoff model for BESS operation and calculated utilization factors for common applications.
result BESS shows higher potential in providing frequency support services, especially in Central Western and Northern Europe.
The Hawking energy is nonnegative and rigid on area-constrained surfaces in general relativity.
problem The rigidity and positivity of the Hawking energy on specific surfaces in general relativity.
method Evaluation of the Hawking energy on area-constrained critical surfaces under the dominant energy condition.
result The Hawking energy is nonnegative and rigid on area-constrained surfaces, including charged and cosmological constant variants.