We show that the circular hydraulic jump can be qualitatively understood using simplified equations of shallow-water type which include viscosity. find outer solutions become singular at a finite radius and this lack asymptotic states is general phenomenon associated with radial flow free surface. By connecting inner through shock, we obtain scaling relation for R j jump, ∼ Q ⅝ v ⅜ g ⅛ , where volume flux, kinematic viscosity gravitational acceleration. This valid asymptotically large ....

Spatiotemporally chaotic dynamics of a Kuramoto - Sivashinsky system is described by means an infinite hierarchy its unstable spatiotemporally periodic solutions. An intrinsic parametrization the corresponding invariant set serves as accurate guide to high-dimensional dynamics, and orbit theory yields several global averages characterizing dynamics.

An accurate data-based prediction of the long-term evolution Hamiltonian systems requires a network that preserves appropriate structure under each time step. Every system contains two essential ingredients: Poisson bracket and Hamiltonian. with symmetries, whose paradigm examples are Lie-Poisson systems, have been shown to describe broad category physical phenomena, from satellite motion underwater vehicles, fluids, geophysical applications, complex plasma physics. The in these comes while...

New model equations are derived for dynamics of aggregation finite-size particles. The differences from standard Debye-Hückel and Keller-Segel models that the mobility particles depends on configuration their neighbors linear diffusion acts locally averaged particle density. evolution collapsed states in these reduces exactly to finite-dimensional interacting clumps. Simulations show (clumped) emerge smooth initial conditions, even one spatial dimension. Extensions two three dimensions also...

This paper develops a novel probabilistic theory of belief formation in social networks, departing from classical opinion dynamics models both interpretation and structure. Rather than treating agent states as abstract scalar opinions, we model them adoption probabilities with clear decision-theoretic meaning. Our approach replaces iterative update rules fixed-point formulation that reflects rapid local convergence within neighborhoods, followed by slower global diffusion. We derive matrix...

This paper develops a novel probabilistic theory of belief formation in social networks, departing from classical opinion dynamics models both interpretation and structure. Rather than treating agent states as abstract scalar opinions, we model them belief-adoption probabilities with clear decision-theoretic meaning. Our approach replaces iterative update rules fixed-point formulation that reflects rapid local convergence within neighborhoods, followed by slower global diffusion. We derive...

A jet of fluid flowing down a partially wetting inclined plane usually meanders. In this paper, we demonstrate that meandering on smooth can be suppressed by maintaining constant volume flow rate. the absence meandering, experimentally observe developing braided structure with non-monotonic width. This pattern is theoretically explained as result interplay between surface tension tends to narrow and inertia drives width expand. The theory also predicts bifurcation braiding regime...

The Euler-alpha and the vortex blob model are two different regularizations of incom- pressible ideal fluid flow. Here, a regularization is smoothing operation which controls velocity in stronger norm than . inviscid version Lagrangian averaged Navier–Stokes-alpha turbulence model. was introduced to regularize flows. This paper presents both models within one general framework, compares results when applied planar axisymmetric filaments sheets. By certain measures, closer unregularized flow...