Related papers: Time-dependent gradient curves on CAT(0) spaces
The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence…
This work is the second part of a program initiated in arXiv:2111.13258 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in metric spaces.…
It is well-known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…
Gradient descent, or negative gradient flow, is a standard technique in optimization to find minima of functions. Many implementations of gradient descent rely on discretized versions, i.e., moving in the gradient direction for a set step…
We study complex surfaces with locally CAT(0) polyhedral Kahler metrics and construct such metrics on CP^2 with various orbifold structures. In particular, in relation to questions of Gromov and Davis-Moussong we construct such metrics on a…
In this paper, we establish equiform differential geometry of space and timelike curves in 4-dimensional Minkowski space. We obtain some conditions for these curves. Also, general helices with respect to their equiform curvatures are…
We introduce Gromov-Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov-Witten invariants with naive tangency conditions in terms of…
We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An…
Chow and Hamilton introduced the cross curvature flow on closed 3-manifolds with negative or positive sectional curvature. In this paper, we study the negative cross curvature flow in the case of locally homogenous metrics on 3-manifolds.…
Examples are given of the creation of closed timelike curves by choices of coordinate identifications. Following G\"odel's prescription, it is seen that flat spacetime can produce closed timelike curves with structure similar to that of…
In the present paper, we study the Myrzakulov-XIII (M-XIII) equation geometrically. From the geometric point of view, we establish a link of the M-XIII equation with the motion of space curves in the 3-dimensional space $R^{3}$. We also…
We present new abstract results on the interrelation between the minimizing movement scheme for gradient flows along a sequence of Gamma-converging functionals and the gradient flow motion for the corresponding limit functional, in a…
This work presents a generalization of the Kraynik-Reinelt (KR) boundary conditions for nonequilibrium molecular dynamics simulations. In the simulation of steady, homogeneous flows with periodic boundary conditions, the simulation box…
The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present…
The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of…
We study the high-frequency limit of non-autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time-dependent perturbation term which might oscillate in a rapid way, but fulfills a certain Lipschitz…
Reminiscent of physical phase transitions separatrices divide the phase space of dynamical systems with multiple equilibria into regions of distinct flow behavior and asymptotics. We introduce complex time in order to study corresponding…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…