Related papers: Predicting Uncertainty in Geometric Fluid Mechanic…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…
We develop a general formalism for introducing stochastic fluctuations around thermodynamic equilibrium which takes into account, for the first time, recent developments on the causality and stability properties of relativistic hydrodynamic…
In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the…
Functional integral representations for solutions of the motion equations for wall-bounded incompressible viscous flows, expressed (implicitly) in terms of distributions of solutions to stochastic differential equations of McKean-Vlasov…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
In this paper, particle physics concepts are blended into a field theory for macroscopic phenomena: Fluid mechanics is enhanced by anticommuting Grassmann variables to describe vorticity, while an additional interaction for the Grassmann…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
Humans can easily describe, imagine, and, crucially, predict a wide variety of behaviors of liquids--splashing, squirting, gushing, sloshing, soaking, dripping, draining, trickling, pooling, and pouring--despite tremendous variability in…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…
The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the…
We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the…
Uncertainty plays a key role in future prediction. The future is uncertain. That means there might be many possible futures. A future prediction method should cover the whole possibilities to be robust. In autonomous driving, covering…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…