Study on wave-breaking phenomena in solutions of the Camassa-Holm equation.
problem Wave-breaking phenomena in solutions of the Camassa-Holm equation.
method Investigation of pseudospherical surfaces and singularities of the metric.
result The metric blows up if and only if the solution breaks in finite time.
A discrete method approximates hyperbolic curvature flow in the plane.
problem Modeling wave phenomena in solid-liquid interfaces.
method Semidiscrete finite difference method for hyperbolic curvature flow.
result Error bounds for natural discrete norms are proven.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this…
A new model uses Lorentz-Finsler geometry to predict wave propagation.
problem Modeling wave propagation in anisotropic and rheonomic media.
method Identifying wave trajectories as lightlike pregeodesics of a specific Lorentz-Finsler metric, solving ODE systems.
result Wave trajectories can be easily computed in real time.
Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.
problem Analyzing decay and non-decay rates of solutions to the massless Vlasov equation on Reissner-Nordström spacetimes.
method Quantitative analysis of geodesic flow and comparison to wave equation instability results.
result Exponential decay rates in subextremal cases and polynomial rates in extremal cases, with non-decay of transversal derivatives in extremal cases.
We illustrate the flow or wave character of the metrics and curvatures of evolving manifolds, introducing the Riemann flow and the Riemann wave via the bialternate product Riemannian metric. This kind of evolutions are new and very natural to understand certain flow or wave phenomena in the nature as well as the geomet…
Study uses DMD to analyze oceanic features in Strait of Gibraltar.
problem Understanding complex oceanic features in Strait of Gibraltar.
method Dynamic Mode Decomposition (DMD) applied to 3D MIT general circulation model simulations.
result Unveiled new elements and dynamics of the Strait of Gibraltar, including a secondary gyre and wave propagation.
Wave maps can have multiple bubbling solutions at blow-up points.
problem Non-uniqueness of bubbling solutions in wave maps.
method Example construction of multiple bubbling solutions.
result First known example of non-uniqueness of bubbling for dispersive equations.
This paper addresses parameter estimation for wave equations with Markovian switching.
problem Parameter estimation for wave equations with abrupt changes.
method Bayesian statistical framework using discrete sparse Bayesian learning.
result Strong performance in parameter estimation for variable coefficient PDEs.
Paper introduces ML tools for guided wave behaviour in composite materials.
problem Difficult assessment of guided wave behaviour in complex materials.
method Data-driven model using Gaussian processes with physical constraints.
result Structured machine learning models offer advantages like extrapolation and physical interpretation.
New method for efficient inference over complex parameter spaces.
problem Challenges in Bayesian inference for high-dimensional, intractable likelihoods.
method Arbitrary Marginal Neural Ratio Estimation (AMNRE) for simulation-based inference.
result Efficient inference over arbitrary subsets of parameters without numerical integration.
The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covarianc…
A Global Navigation Satellite System (GNSS) uses a constellation of satellites around the earth for accurate navigation, timing, and positioning. Natural phenomena like space weather introduce irregularities in the Earth's ionosphere, disrupting the propagation of the radio signals that GNSS relies upon. Such disruptio…
Survey on stability of Minkowski spacetime in relativity.
problem Nonlinear stability of Minkowski spacetime in general relativity.
method Decay assumptions, geometric foliations, energy identities, and gauge choices.
result Understanding of decay, dispersion, and geometry-analysis interplay.
Develops a climate risk model for asset managers.
problem Climate-related risks affecting asset performance and productivity.
method Uses the Vasicek model with downward jumps to represent climate impacts on asset dynamics.
result Expected losses increase over time due to climate-related extreme events.
In this paper we prove that all initially-smooth solutions of the Euler-Weil-Petersson equation, which describes geodesics on the universal Teichmüller space under the Weil-Petersson metric, will remain smooth for all time. This extends the work of Escher-Kolev for strong Riemannian metrics to the borderline case of $H…
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
problem Interaction of three impulsive gravitational waves in Einstein vacuum equations.
method Geometric estimates and wave estimates to prove local solution and continuity.
result Local solution to Einstein vacuum equations with three impulsive gravitational waves, Lipschitz continuity.
New Galilean spacetimes found as pp-wave reductions.
problem Understanding isotropic homogeneous Galilean spacetimes.
method Null reductions of pp-wave spacetimes.
result Found novel torsional Galilean spacetimes.
Analyzes Gerstner's trochoidal waves and their geometric properties.
problem Understanding the geometry and kinematics of trochoidal waves.
method Derives velocity and arc length conditions for cycloidal, curtate, and prolate trochoids using Galilean transformations.
result Conditions for arc lengths of prolate and curtate trochoids to coincide over a wave cycle.
Wave fronts on certain surfaces become dense.
problem Density of wave fronts on surfaces.
method Proof of density for specific surfaces.
result Wave fronts become dense on flat torus, square billiard, Klein bottle, and cube surface.
Analyzes properties of stiffness tensors for elastic wave imaging.
problem Characterizing stiffness tensor fields for elastic wave imaging.
method Finsler-geometric methods applied to anisotropic stiffness tensor fields.
result Conditions for Finsler-geometric methods to be applicable.
Deep learning model predicts wind-wave relationship.
problem Characterize ocean wave climate for engineering applications.
method Two-stage deep learning model: CNN for spatial features, LSTM for temporal dependencies.
result Predicts spatio-temporal relationship between wind and significant wave height.
Impulsive waves contradict a 1962 conjecture about pp-waves.
problem The failure of the Ehlers--Kundt conjecture in the impulsive case.
method Summarized completeness results for impulsive wave spacetimes.
result Impulsive pp-waves are complete, contradicting the conjecture.
Extends Penrose limit to Finsler spacetimes.
problem Extending Penrose limit to Finsler spacetimes.
method Introducing lightlike coordinates and adapting Lorentzian pp-wave definition.
result New examples of Finsler pp-waves presented.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
Classifies solutions to vacuum weighted Einstein equations on pr-waves.
problem Classifying solutions to vacuum weighted Einstein field equations on pr-waves.
method Classifying solutions using smooth metric measure spacetimes of dimension 4.
result Provides examples of solutions with special geometric properties.
Study compact plane waves, showing they are essentially standard.
problem Understanding the topology and dynamics of compact plane waves.
method Analyzing quotients of homogeneous plane waves by discrete subgroups.
result Compact quotients of homogeneous plane waves are essentially standard.
New method finds precise late-time behavior of wave equations.
problem Analyzing late-time behavior of wave equations with inverse-square potentials.
method Physical-space-based method for deriving late-time asymptotics.
result Sharp, uniform decay estimates in time for asymptotic late-time tails.
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of the initial wave fronts.
Paper explores non-uniqueness and uniqueness class for wave equations on graphs.
problem Non-uniqueness of solutions to wave equations on infinite graphs.
method Analyticity of solutions in the uniqueness class, extension to a wide class of linear evolution equations.
result Sharp uniqueness class for solutions of wave equations on graphs.
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
New metrics link Kähler and pp-wave spacetimes.
problem Connecting Kähler and pp-wave spacetimes.
method Constructing families of complete almost Kähler metrics by deforming pp-waves.
result Established a one-to-one correspondence between almost Kähler metrics and pp-wave spacetimes.
New method detects spike-and-wave epileptiform discharges using Kendall's Tau-b.
problem Detecting spike-and-wave epileptiform discharges in EEG signals.
method Proposes a new method based on Kendall's Tau-b coefficient.
result High Specificity and rule in (SpPIn) for spike-and-wave discharge detection.
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on 2-forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classic…
The paper shows how null hypersurfaces behave in Lorentz-Minkowski space.
problem Understanding null hypersurfaces in Lorentz-Minkowski space.
method Analyzing L-complete null hypersurfaces as wave fronts in Euclidean space. result Most null wave fronts can be realized as restrictions of certain L-complete null wave fronts. New metrics constructed dual to specific wave-like geometries.
problem Constructing metrics dual to general plane-fronted wave Lorentzian metrics.
method Explains construction of extremal and non-Kähler almost-Kähler metrics.
result Constructs canonical almost-Kähler metrics dual to general plane-fronted wave Lorentzian metrics.
Study pp-waves with lightlike parallel spinors in vacuum spacetimes.
problem Characterize pp-waves with lightlike parallel spinors in vacuum spacetimes.
method Parametrize pp-wave spacetimes, show correspondence with Riemannian metrics, prove parallel spinor condition.
result A pp-wave spacetime with a lightlike parallel spinor corresponds to a Ricci-flat metric with a parallel spinor.
Develops methods to construct harmonic and wave maps into variable-curvature surfaces.
problem Limited explicit constructions for harmonic and wave maps in variable-curvature settings.
method Reduction framework for pseudo-Riemannian surfaces, geometric ansatz, first-order ODEs.
result Constructs explicit harmonic and wave maps into ellipsoids, hyperboloids, and Schwarzschild exterior.
Framework augments physical models with deep learning for complex dynamics forecasting.
problem Forecasting complex dynamical phenomena with partial knowledge.
method APHYNITY framework: decomposes dynamics into physical and data-driven components.
result Framework accurately forecasts system evolution and identifies relevant parameters.
Unique solutions found for wave-like decaying null infinity equations.
problem Wave-like decaying null infinity equations with spherically symmetric Einstein-scalar-field.
method Local and global unique solutions for small initial data.
result Sharp decaying condition for unique solutions.
The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spaceti…
Measuring wave sources uniquely identifies manifold properties.
problem Determining Riemannian manifold structure from wave observations.
method Semilinear wave equation measurements at a single point.
result Topological, differential, and geometric structure can be inferred.
We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the beh…
Shorter proof for wave front length in Euclidean disk
problem Wave front length in Euclidean disk
method Shorter proof and computation of oscillating corrections
result Linear asymptotics of wave front length in large time
Study finds rigid submanifolds in spacelike waves under specific conditions.
problem Understanding rigidity of submanifolds in spacelike waves.
method Proves submanifolds are contained in characteristic lightlike hypersurfaces under certain conditions.
result Complete codimension two submanifolds are wavefronts under specific conditions.
The wave trace of certain convex domains can be smooth near some points in the length spectrum.
problem Understanding the relationship between the wave trace and the length spectrum of convex domains.
method Constructing silent periodic billiard orbits with the same length but different Maslov indices, using a microlocal parametrix for wave invariants.
result The wave trace can be smooth near some points in the length spectrum, showing potential limitations for inverse spectral problems.
Initial data for pp-wave spacetimes constructed in 4D.
problem Characterizing initial data for pp-wave spacetimes. method Constructs a vacuum initial data set with extra conditions related to CKID.
result Data development is a subset of a vacuum pp-wave.