Related papers: Simple Gradient Flow Equation for the Bounce Solut…
Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on $[0,+\infty )$, which has an absorbing barrier at zero. Then one can define its dual stochastic flow. In \cite{AW}, Akahori…
We study the gradient-flow structure of a non-Newtonian thin film equation with power-law rheology. The equation is quasilinear, of fourth order and doubly-degenerate parabolic. By adding a singular potential to the natural Dirichlet…
In his 1977 paper on vacuum decay in field theory: The Fate of the False Vacuum, Coleman considered the problem of a single scalar field and assumed that the minimum action tunnelling field configuration, the bounce, is invariant under O(4)…
"Ground effect" refers to the enhanced performance enjoyed by fliers or swimmers operating close to the ground. We derive a number of exact solutions for this phenomenon, thereby elucidating the underlying physical mechanisms involved in…
We explore the possibility of avoiding cosmological singularity with a bounce solution in the early Universe. The main finding is that simple and well-known semiclassical correction, which describes the mixing of radiation and gravity in…
This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss…
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…
In the decay process of metastable vacua in quantum field theories, the bounce solution, a classical solution in Euclideanized theories, is helpful in calculating the decay rate. Recently, the bounce solution with a conical singularity has…
I present a solution to the full Einstein-fluid equations representing a self-gravitating Bjorken flow. The motion and the geometry become inhomogeneous in the plane transversal to the flow and the energy density profile acquires, due to…
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solution, inspired by the theory of curves of maximal slope, and…
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…
We study zero-temperature false vacuum decay in $D$ compact spatial dimensions and show that for volumes below a critical value a new bounce solution, different from Coleman's celebrated $O(D)$ bubble, mediates the decay process, and…
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient…
The spectrum of small perturbations about oscillating bounce solutions recently discussed in the literature is investigated. Our study supports quite intuitive and expected result: the bounce with N nodes has exactly N homogeneous negative…
A tunneling bounce driving the decay of a metastable vacuum must respect an integral constraint dictated by simple scaling arguments that is very useful to determine key properties of the bounce. After illustrating how this works in a…
The tunneling potential formalism, an alternative to the standard Coleman Euclidean approach, offers in a natural way a unified view of vacuum decays. In particular, I show in this talk how Coleman's bounce is just a member of a continuous…
A bouncing universe is a viable candidate to solve the initial singularity problem. Here we consider bouncing solutions in the context of $f(R,\mathcal{G})$ gravity by using an order reduction technique which allows one to find solutions…
We investigate bounce cosmological models in the presence of a viscous fluid, making use of generalized holographic cutoffs introduced by Nojiri and Odintsov (2017). We consider both an exponential, a power-law, and a double exponential…
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples…
We propose a quasi-Grassmannian gradient flow model for eigenvalue problems of linear operators, aiming to efficiently address many eigenpairs. Our model inherently ensures asymptotic orthogonality: without the need for initial…