Study geometric quantum confinement on special incomplete Riemannian manifolds.
problem Characterize quantum confinement on Grushin-type manifolds.
method Constant-fibre direct integral scheme combined with Weyl's analysis.
result Fully characterizes essential self-adjointness of Laplace-Beltrami operator.
This paper identifies criteria for quantum confinement on non-complete Riemannian manifolds.
problem Quantum confinement on non-complete Riemannian manifolds with potential and degenerate measures.
method Identification of an effective potential Veff and formulation of criteria for quantum confinement. result Simple criteria for quantum confinement are formulated, allowing for measures with degeneracies or singularities near the metric boundary.
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.
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.
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…
Estimates classical potential from stock price data using quantum mechanics.
problem Estimating classical potential from empirical stock price data.
method Quantum mechanical model of stock price distribution, estimating potential from wave function.
result Suggests methods to evaluate classical potential for Schrodinger equation.
Quantum model explains stock market price behavior.
problem Classical models fail to explain stock market dynamics.
method Quantum particle analogy for stock prices.
result Quantum model explains various market phenomena.
We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrodinger equation which is valid e.g. in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, a…
Study reveals weak knotting in confined polymers, not dominated by any single knot type.
problem Characterizing knotting in open, confined polymers.
method Modeling open curves as virtual knots, comparing lattice walks and ideal chains in confined and unconfined conditions.
result Weak knotting is a common feature in confined polymers, not dominated by any single knot type.
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.
Study on curves minimizing bending energy in confined spaces.
problem Finding optimal shapes of curves within bounded domains.
method Existence, regularity, and structural properties of minimizers proven.
result Existence of minimizers, convexity of minimizers in convex domains, and examples of non-convex minimizers.
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.
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 C∗-simplicity for groups without certain subalgebras.
problem Characterizing C∗-simplicity of groups. method Introducing confined subalgebras and Uniformly Recurrent States.
result A countable discrete group is C∗-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.
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…
This paper computes fixed point Floer cohomology for Dehn twists on surfaces.
problem Computing fixed point Floer cohomology for Dehn twists.
method Developed tools for computing fixed point Floer cohomology and product for Dehn twists in all dimensions.
result Splitting of the product and differential into local and Morse-theoretic contributions.
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.
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.
This work uses scientific constraints to validate neural network predictions in fusion physics.
problem Verifying the scientific plausibility of neural network predictions in fusion physics.
method Using known scientific constraints as a validation tool.
result Validated neural network predictions in fusion physics using scientific constraints.
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.
Minimal submanifolds either fill space or are confined with geometric restrictions.
problem Understanding the behavior of minimal submanifolds in space.
method A dichotomy principle and volume doubling theorem.
result Quantitative restrictions on confined minimal submanifolds, including volume growth and optimal density rates.
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.
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.
This thesis explores geometric properties of curves and their applications in quantum mechanics.
problem Characterizing spherical curves and understanding quantum dynamics of constrained particles.
method Developing Rotation Minimizing frames and applying them to spherical curves and quantum mechanics.
result RM frames provide a new approach to characterize spherical curves and study quantum dynamics.
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.
We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel tran…
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.
Compactification of AdS5 allows studying meson behavior in QCD.
problem Understanding meson behavior in Quantum Chromodynamics (QCD).
method Deforming AdS5 metric to model Coulomb interaction between charges.
result Proposed conformal deformation provides a quantum mechanical description of mesons.
We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is comp…
Seq2seq models predict complex multi-physics systems' time evolution.
problem Predicting the time-evolution of complex multi-physics systems.
method Sequence-to-sequence models applied to multi-physics simulations.
result Seq2seq models accurately emulate complex systems and predict their evolution.
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…
Transfer learning improves fusion simulation accuracy.
problem Calibrate fusion simulation models to experimental data.
method Hierarchical transfer learning using deep neural networks.
result Calibrated models predict Omega experiments more accurately.
Modeling GDP growth rates using Lévy flights with confining potential.
problem Understanding the impact of firm size fluctuations on GDP.
method Combining microscopic firm growth rates with macroscopic GDP, using Lévy-stable fluctuations and a confining potential.
result The model accurately predicts 200 years of US GDP growth rates.
New theorem links symmetries to first integrals in plasma physics.
problem Understanding the relationship between symmetries and first integrals in divergence-free fields.
method Developed a Noether-type Theorem reformulation for three-dimensional divergence-free vector fields.
result Converse of the Noether-type Theorem holds on the toroidal region, proving the existence of flux coordinates.
We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, o…
Deep learning compares turbulence models in plasma physics.
problem Predicting edge plasma turbulence in magnetic fusion reactors.
method Physics-informed deep learning framework for comparing two-fluid and gyrokinetic models.
result Good overall agreement between two-fluid theory and gyrokinetic models in turbulent field fluctuations.
A new sampler and temperature estimation method enable efficient learning of Boltzmann Machines.
problem Efficient learning of Boltzmann Machines (BMs) is challenging due to high training costs and difficulty in parallelization.
method Proposed a new Boltzmann sampler (Langevin SB, LSB) and an efficient method (Conditional Expectation Matching, CEM) for estimating inverse temperature.
result Established an efficient learning framework (Sampler-Adaptive Learning, SAL) for BMs with greater expressive power than Restricted Boltzmann Machines (RBMs).
New bounds on stick number of knots found using random polygon generation.
problem Understanding the minimum number of segments needed to build a polygonal knot.
method Monte Carlo approach to generating and analyzing large ensembles of random polygons.
result Improved bounds on stick number for over 40% of knots with 10 or fewer crossings.
The study examines linking numbers and writhes in random graph embeddings within a cube.
problem Modeling entanglements of polymers in confined spaces.
method Analysis of linking numbers and writhes in random linear embeddings of complete graphs and graphs on n vertices.
result Mean sum of squared linking numbers and writhes are of the order of θ(n(n!)) for random embeddings.
Study of geometry-induced potentials for curved regions in 3D space.
problem Finding a curved region with a prescribed geometry-induced potential.
method Formalism to deduce a meaningful Hamiltonian for confinement, solving for curves and surfaces using PDEs and ODEs.
result Existence of geometry-induced bound and localized states for helicoidal surfaces.
Wealth redistribution through Fokker-Planck equation controls preserves Gini coefficient.
problem Preserving Gini coefficient through proportional wealth tax.
method Formulating optimal redistribution as a control problem for Fokker-Planck equation.
result Progressive taxes redistribute within policy-relevant timescales.
We prove mean curvature estimates and a Jorge-Koutroufiotis type theorem for submanifolds confined into either a horocylinder of N X L or a horoball of N, where N is a Cartan-Hadamard manifold with pinched curvature. Thus, these submanifolds behave in many respects like submanifolds immersed into compact balls and into…
We study the mean curvature flow of complete space-like submanifolds in pseudo-Euclidean space with bounded Gauss image, as well as that of complete submanifolds in Euclidean space with convex Gauss image. By using the confinable property of the Gauss image under the mean curvature flow we prove the long time existence…
Researchers successfully implemented quantum autoencoders using quantum adders in a cloud quantum computer.
problem Reducing resource usage in quantum computations.
method Experimental implementation of quantum autoencoders using approximate quantum adders in a cloud quantum computer.
result Experimental fidelities are in good agreement with theoretical predictions, proving the feasibility of quantum autoencoders via quantum adders.