Study proves fluid limits of fragmented limit-order markets.
problem Modeling fragmented limit-order markets with small and frequent orders.
method Proved convergence of discrete system to fluid limit characterized by coupled nonlinear ODEs.
result Fluid system converges to stationary equilibrium state over time.
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
The paper models CBF dynamics using queueing theory and insurance risk models.
problem Understanding and optimizing the operation of community bail funds.
method Combining queueing theory with classic insurance risk models.
result A fluid limit for the blocking model of CBF operations.
The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the…
Smartfluidnet accelerates Eulerian fluid simulation with neural networks.
problem Current neural network methods for Eulerian fluid simulation lack flexibility and generalization.
method Smartfluidnet automates model generation and dynamic switching to meet user requirements.
result Smartfluidnet achieves 1.46x and 590x speedup compared to state-of-the-art models, with better simulation quality.
We study the free boundary Euler equations in two spatial dimensions. We prove that if the boundary is sufficiently regular, then solutions of the free boundary fluid motion converge to solutions of the Euler equations in a fixed domain when the coefficient of surface tension tends to infinity.
In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a c…
New minimal surfaces found from vortex crystals.
problem Minimal surfaces and vortex crystals.
method Gluing helicoids into minimal surfaces.
result New minimal surfaces and vortex crystals discovered.
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 (DeePN2) accurately predicts fluid behavior without empirical closures. We evaluate how modern outlier detection methods perform in identifying outliers in e-commerce conversion rate data. Based on the limitations identified, we then present a novel method to detect outliers in e-commerce conversion rate. This unsupervised method is made more business relevant by letting it automatically a…
We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.
Proves existence and uniqueness of rotating fluid bodies in GR to second order.
problem Understanding rotating fluid bodies in GR, especially beyond Newtonian limits.
method Second order perturbation theory, derived from first principles, with rigidly rotating finite perfect fluid ball assumptions.
result Equatorially symmetric spacetime determined by central pressure and uniform angular velocity.
In our previous article [Rad16], we investigated the asymptotic behaviour of orthogonal Bianchi class B perfect fluids close to the initial singularity and proved the Strong Cosmic Censorship conjecture in this setting. In several of the statements, the case of a stiff fluid had to be excluded. The present paper fills …
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
Novel deep learning approach for fast, differentiable fluid simulations.
problem Challenges in solving incompressible fluid dynamics equations efficiently.
method Physics-constrained training approach for convolutional neural networks.
result Trained models can handle various fluid phenomena and offer fast simulations.
Model simulates correlation emergence in two coupled limit order books.
problem Modeling correlation emergence in coupled limit order books.
method Simulated two coupled diffusive limit order books using random walks in the fluid limit, with trader interactions.
result Demonstrated the recovery of an Epps effect from the model.
FLUID-LLM uses LLMs to predict fluid dynamics with improved accuracy.
problem Leveraging LLMs for CFD due to their pattern recognition abilities but struggles with fluid dynamics complexities.
method Combines pre-trained LLMs with spatiotemporal-aware encoding to predict unsteady fluid dynamics.
result Significant performance improvements in CFD predictions across various datasets.
New approach links 2D fluid dynamics to matrix theory.
problem Understanding swirling patterns in 2D fluids.
method Matrix hydrodynamics linking 2D fluid dynamics to matrix theory.
result Established connections between 2D hydrodynamics and matrix Lie theory.
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of Rn, thi…
On curved spaces, viscous fluids reach equilibrium quickly.
problem Thermalization of viscous fluids on negatively curved manifolds.
method Stochastic Navier-Stokes equations with kinematically selected deformation Laplacian.
result Exponential thermalization rate of $2νλ_\Def$.
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a…
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
problem Characterizing pseudosymmetric spacetimes as perfect fluids.
method Analyzes generalized Robertson-Walker spacetimes, conformally flat spacetimes, and dust fluids.
result Conditions for pseudosymmetric spacetimes to be perfect fluids are established.
New method efficiently simulates fluid flows across various conditions.
problem High computational cost in simulating fluid flows.
method Parameter-conditioned sequential generative modeling of neural networks.
result Trained models simulate fluid flows at orders of magnitude faster than traditional methods.
Derives a fluid model for fish swarming in arbitrary dimensions.
problem Modeling fish swarming behavior in various dimensions.
method Develops a novel n-dimensional model using bundle geometry and variational formulation. result Derives the self-organized hydrodynamic model from the interacting particle system.
The study examines properties of perfect fluid spacetimes in Einstein's theory.
problem Analyzing curvature properties of perfect fluid spacetimes.
method Assuming perfect fluid as the source, the paper investigates solutions to Einstein's field equations.
result Properties of perfect fluid spacetimes are explored in the context of Einstein's theory.
This research smooths out fluid equations to avoid sudden shocks.
problem Formation of shock singularities in compressible fluid equations.
method Information geometric regularization of unidimensional pressureless Euler equations.
result Smooth global solutions without artificial viscosity.
The study identifies unique fluid flow patterns.
problem Understanding incompressible fluid flows with straight streamlines.
method Local differential geometry of line congruences to integrate Euler equations.
result Only specific fluid flows are possible with straight streamlines.
This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of…
Simulates financial market orders using anomalous diffusion models.
problem Anomalous diffusion in financial market order dynamics.
method Discrete Time Random Walk with Sibuya waiting times, non-uniform sampling, and cubic spline interpolation.
result Demonstrates price impact for different forcing functions and model parameters.
Study on static perfect fluid space-time geometry and boundary estimates.
problem Investigate the geometry and boundary properties of static perfect fluid space-time.
method Used generalized Reilly's formula to establish geometric inequalities and boundary estimates.
result Obtained new boundary estimates involving the Brown-York mass and first eigenvalue of the Jacobi operator.
Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.
Paper develops a new fluid flow model with energy exchange through boundaries.
problem Modeling ideal fluid flow with energy exchange through boundaries.
method Port-Hamiltonian model based on Stokes-Dirac structures.
result Wide range of fluid dynamical systems can be achieved with this model.
Survey on matrix hydrodynamics, a 2D fluid model.
problem Modeling 2D incompressible fluids.
method Spatial discretization via quantization theory.
result Basic demonstration of matrix hydrodynamics.
Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
problem Lack of rotational symmetry in machine learning models for fluid systems.
method Introduces RotEqNet, a network that guarantees rotation-equivariance for high-order tensors.
result RotEqNet reduces errors and maintains rotation-equivariance in fluid systems.
Study of k-almost Yamabe solitons in perfect fluid spacetimes.
problem Analyzing k-almost Yamabe solitons in perfect fluid spacetimes. method Examined perfect fluid spacetimes and k-almost Yamabe solitons using Einstein field equations. result Characterized properties of k-almost Yamabe solitons in perfect fluid spacetimes. We proposed a novel graph convolutional neural network that could construct a coarse, sparse latent point cloud from a dense, raw point cloud. With a novel non-isotropic convolution operation defined on irregular geometries, the model then can reconstruct the original point cloud from this latent cloud with fine detail…
This research optimizes fluid-dynamic designs using deep learning and active learning.
problem Expensive and limited empirical design verification for fluid dynamics.
method Applied a deep learning architecture to predict and optimize fluid dynamics performance.
result Reduced the number of required simulation data points from ~8000 to 625.
Generative models improve carbon storage site prediction using Bayesian inversion.
problem Predicting suitable geologic sites for long-term carbon dioxide storage.
method Generative adversarial networks and Bayesian inversion to condition models on physical measurements and historic data.
result Improved resolution of carbon dioxide storage capacity forecasts.
Geometric Hydrodynamics tackles open problems in fluid dynamics.
problem Open problems in fluid dynamics and invariant metrics.
method Variational settings, models for invariant metrics, Cauchy and boundary value problems.
result New constructions and recent developments in fluid dynamics.
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
Incompressible fluid dynamics on special manifolds.
problem Fluid dynamics on specific geometric manifolds.
method Analyzes G-invariant vector fields on compact manifolds. result Shows existence of smooth solutions to Euler equations.
Investigates fluid flow perturbations using geometric theory.
problem Analyzing linear perturbations in non-equilibrium fluid flows.
method Uses second order variations of the action and Jacobi fields.
result Demonstrates numerical simulations of perturbation dynamics.
We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresh…
The paper explores the geometric properties of fluid flows and their symmetries.
problem Understanding the geometric properties of fluid flows and their symmetries.
method Analyzing the Euler equation and its relation to geodesic flows on groupoids of multiphase diffeomorphisms.
result Generalized flows, multiphase fluids, and vortex sheets are all geodesics on certain groupoids of multiphase diffeomorphisms.
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.