We present a theory of rare events and derive an algorithm to obtain rates from postprocessing the numerical data of a free energy calculation and the corresponding committor analysis. The formalism is based on the division of the saddle region of the free energy profile of the rare event into two adjacent segments called saddle domains. The method is built on sampling the dynamics within these...

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger...

The aim of the following study is to analyze the mechanical efficiency on heart rate frequency and oxygen consumption during exercise bicycle test. The following study included seven respondents (men) aged 19-28 years, all students in the National Sports Academy “Vassil Levski” (Sofia, Bulgaria) – specialists in cycling. During two consecutive days, they were administered to sub maximal bicycle...

BACKGROUND Although various techniques have been described for correction of crooked and saddle nose deformities, these problems are challenging with high recurrence and revision rates. Conventional septal surgery may not be adequate for nose reconstruction in crooked and saddle nose deformities. MATERIALS AND METHODS Between December 2005 and October 2009, six patients with crooked nose and ...

INTRODUCTION The purpose of this study was to investigate the influence of gender, power, hand position, and ischial tuberosity (IT) width on saddle pressure during seated stationary cycling. METHODS Twenty-two experienced cyclists (11 males and 11 females) were fitted to an adjustable stationary bicycle and pedaled at 100 and 200 W in both the tops and drops hand positions. An instrumented p...

We propose a model-free shrinking-dimer saddle dynamics for finding any-index points and constructing the solution landscapes, in which force standard is replaced by surrogate model trained Gassian process learning. By this means, exact form of no longer necessary such that could be implemented based only on some observations force. This data-driven approach not avoids modeling procedure diffic...

Riemann’s way to calculate his zeta function on the critical line was based on an application of his saddle-point technique for approximating integrals that seems astonishing even today. His contour integral for the remainder in the Dirichlet series for the zeta function involved not an isolated saddle, nor a saddle near a pole or an end-point or several coalescing saddles, but the configuratio...

We consider the condensation transition of microemulsion droplets of oil which are dispersed in water in the presence of surfactant. Since a macroscopic oil phase is formed due to this transition, it is called "emulsification failure." Based on the free energy approach, we determine the transition lines between the spherical and the cylindrical droplet phases as well as the phase boundary lines...

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NH...

CONTEXT It is not clear how noncyclists control joint power and kinematics in different mechanical setups (saddle height, workload, and pedaling cadence). Joint mechanical work contribution and kinematics analysis could improve our comprehension of the coordinative pattern of noncyclists and provide evidence for bicycle setup to prevent injury. OBJECTIVE To compare joint mechanical work distr...