arXiv research

The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …

This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by …

We formulate and analyze a multi-agent model for the evolution of individual and systemic risk in which the local agents interact with each other through a central agent who, in turn, is influenced by the mean field of the local agents. The central agent is stabilized by a bistable potential, the only stabilizing force…

Improved CG force-field learning from all-atom data.

New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.

Study calculates curvature for fluid dynamics group, proving positivity.

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…

In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian cur…

Curve shortening flow shrinks curves to points under certain conditions.

In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a long-time smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the extern…

The paper establishes a connection between force-free fields and conformally geodesic fields.

Machine learning generates coarse-grained force fields for molecular dynamics.

Neural network models colloidal particle dynamics in non-equilibrium systems.

The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with…

Proposes linking energy and force uncertainty in deep learning potentials.

This paper presents a model of capital accumulation for a large number of heterogenous producer-consumers in an exchange space in which interactions depend on agents' positions. Each agent is described by his production, consumption, stock of capital, as well as the position he occupies in this abstract space. Each age…

Develops Hamiltonian Score Matching and Generative Flows for machine learning.

BoostMD accelerates molecular dynamics simulations by 8x with ML force fields.

Study active nematic forces on curved surfaces, revealing new coupling mechanisms.

In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the $N$-body problem with general masses and any $1/r^α$ potential with $α> 0$. We also observe dynamical consequences of these curvature values for relati…

We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network model of the potential and then applies an equation discovery technique to extract…

Study physical work done by isotropic vector forces along isotropic curves.

New method speeds up kernel-based machine learning for force field reconstruction.

AniDS improves molecular force field modeling by learning anisotropic noise.

MACE uses higher-order messages to create fast, accurate force fields.

Model shows PoS networks can be captured by external finance, leading to centralization.

Flow of curves with curvature and forcing vector field exists.

Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field…

We determine the universal central extension of the Lie algebra of hamiltonian vector fields, thereby classifying its central extensions. Furthermore, we classify the central extensions of the Lie algebra of symplectic vector fields, of the Poisson Lie algebra, and of its compactly supported version.

New framework embeds physics in coarse-grained models without big data.

CAMEL embeds data into a manifold using curvature-augmented forces.

Paper introduces a PDE-free method for decomposing forces in any dimension.

In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called the geodesic $k$-vector field, analogous to the ordinary geodesic field and which …

We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow, except in cases where the underlying manifold is topologically simple. Furtherm…

GDML learns effective CG models from all-atom data.

The Lorentz force equations provide a partial description of the geodesic motion of a charged particle on a four-manifold. Under the hypothesis that Maxwell's equations express symmetry properties of the Ricci tensor, the full electromagnetic connection is determined. From this connection, the fourth equation of the ge…

Researchers solve a 25-year-old conjecture about vector fields.

MACE architecture outperforms alternatives in various molecular and materials science tasks.

Dataset for rainfall modeling in central Europe from 1981-2011.

In this review paper, we present several results on central extensions of the Lie algebra of symplectic (Hamiltonian) vector fields, and compare them to similar results for the Lie algebra of (exact) divergence free vector fields. In particular, we comment on universal central extensions and integrability to the group …

The dynamics defined by a force field which is positively homogeneous of degree $-3$ can always be reduced, by simply constraining it. The dimension of the phase space is reduced by two dimensions, while it may only be reduced by one dimension if the degree of homogeneity is different from $-3$. This remark is an elega…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form of flows of a given geodesic curvature is proposed. For illustration, the proble…

Centralized exchanges influence staking behavior and decentralization in Proof of Stake blockchain ecosystems.

We provide a benchmark dataset for hand gesture recognition using force myography.

This work discovers latent field effects governing interacting dynamical systems.

We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish …

Geometrically transforms nonconservative dynamics to linearize Kepler and Manev systems.