Related papers: Bounce Configuration from Gradient Flow
We present an algorithm to analyze numerically the bounce solution of first-order phase transitions. Our approach is well suited to treat phase transitions with several fields. The algorithm consists of two parts. In the first part the…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which…
A dynamical system is defined in terms of the gradient of a payoff function. Dynamical variables are of two types, ascent and descent. The ascent variables move in the direction of the gradient, while the descent variables move in the…
It has been shown that a water drop can bounce persistently, when thrown on a super-hydrophobic substrate. We present here scaling arguments which allow us to predict the maximal deformation and the contact time of the drop. This approach…
Bio-inspired methods can provide efficient solutions to perform autonomous landing for Micro Air Vehicles (MAVs). Flying insects such as honeybees perform vertical landings by keeping flow divergence constant. This leads to an exponential…
We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no…
Recently, a novel phenomenon is observed for vacuum decay to proceed via classically allowed dynamical evolution from initial configurations of false vacuum fluctuations. With the help of some occasionally developed large fluctuations in…
To achieve point cloud denoising, traditional methods heavily rely on geometric priors, and most learning-based approaches suffer from outliers and loss of details. Recently, the gradient-based method was proposed to estimate the gradient…
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we…
Recent years have seen increased interest in performance guarantees of gradient descent algorithms for non-convex optimization. A number of works have uncovered that gradient noise plays a critical role in the ability of gradient descent…
In this paper, we propose an algorithm for registering sequential bounding boxes with point cloud streams. Unlike popular point cloud registration techniques, the alignment of the point cloud and the bounding box can rely on the properties…
In this work we show a class of oscillating configurations for the evolution of the domain walls in Euclidean space. The solutions are obtained analytically. Phase transitions are achieved from the associated fluctuation determinant, by the…
Several mechanical systems are modeled by the static momentum balance for the displacement $u$ coupled with a rate-independent flow rule for some internal variable $z$. We consider a class of abstract systems of ODEs which have the same…
In this study, we develop an interface-contact simulation framework based on physical criteria and machine-learning-assisted classification to describe coalescence and bouncing within a unified formulation. The framework realizes…
Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit.…
In the standard procedure for calculating the decay rate of a metastable vacuum the solution of the classical Euclidean equation of motion of the background field is needed. On the other hand radiative corrections have to be taken into…
This paper presents a discrete-time passivity-based analysis of the gradient descent method for a class of functions with sector-bounded gradients. Using a loop transformation, it is shown that the gradient descent method can be interpreted…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
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…