There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation. Although saddle foci of index 2 have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper. A novel approach for construc...

Common causes of poor performance in horses include factors related to the horse, the rider and/or the saddle, and their interrelationships remain challenging to determine. Horse-related factors (such as thoracolumbar region pain and/or lameness), rider-related factors (such as crookedness, inability to ride in rhythm with the horse, inability to work the horse in a correct frame to improve cor...

Saddle point search on an energy surface has broad applications in fields like materials science, physics, chemistry, and biology. In this paper, we present the shrinking dimer dynamics (SDD), a dynamic system which can be applied to locate a transition state on an energy surface corresponding to an index-1 saddle point where the Hessian has a negative eigenvalue. By searching for the saddle po...

یکی از عوامل محرک برای ایجاد جریان محوری درون روتور سانتریفیوژ به منظور افزایش عملکرد جداسازی، اسکوپ است. با توجه قرار گرفتن در معرض گاز ماخ بالا، دچار شوک شده و گرادیان‌های شدیدی اتفاق خواهد افتاد. این پژوهش اطراف حالت دوبعدی (r-θ) روش شبیه­سازی مستقیم مونت‌کارلو (DSMC) استفاده حل­گر dsmcFoam فواصل مختلف دیواره شبیه‌سازی نتایج نشان می‌دهد که فاصله کاهش زاویه برخورد اسکوپ، سبب بیشینه دما نیروی ...

BACKGROUND As dental implants receive masticatory stress, the distribution of stress is very important to peri-implant bone homeostasis and implant survival. In this report, we created a saddle-type implant and analyzed its stability and ability to distribute stress to the surrounding bone. METHODS The implants were designed as a saddle-type implant (SI) that wrapped around the alveolar bone,...

In this paper we present a Lagrange-multiplier formulation of discrete constrained optimization problems, the associated discrete-space first-order necessary and sufficient conditions for saddle points, and an efficient first-order search procedure that looks for saddle points in discrete space. Our new theory provides a strong mathematical foundation for solving general nonlinear discrete opti...

Bifurcation theory provides a classification of the expected ways in which the number and/or stability of invariant solutions (‘attractors’ and ‘repellors’) of nonlinear ordinary differential equations may change as parameter values are changed. The most common qualitative changes are ‘saddle-node’ bifurcations, ‘Hopf’ bifurcations, and ‘SNIPER’ bifurcations. At a saddle-node bifurcation, a pai...

In case f0 and C are convex, a variety of primal/dual numerical methods can be used to find the saddle points of a Lagrangian L associated with this problem [4, 7]. These methods take advantage of the fact that the search for the saddle points of L is unconstrained, or conducted over sets much simpler than C. Furthermore, we can introduce penalties on f0 in a way that regularizes L and makes it...

We discuss O(N) invariant scalar field theories in 0+1 and 1+1 space-time dimensions. Combining ordinary “Large N” saddle point techniques and simple properties of the diagonal resolvent of one dimensional Schrödinger operators we find exact non-trivial (space dependent) solutions to the saddle point equations of these models in addition to the saddle point describing the ground state of the th...

Finding multiple local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points known in mathematics as Morse index 1 saddle poin...