Quasi-threshold phenomenon in noise-driven Higgins model

2020 ◽  
Vol 91 ◽  
pp. 105441
Author(s):  
Yang Li ◽  
Jianlong Wang ◽  
Xianbin Liu
Keyword(s):  
Threshold Phenomenon

OPTICAL NONLINEARITY VIA PHONONS AS AN INTERMEDIARY

2001 ◽  
Vol 10 (01) ◽  
pp. 65-77 ◽  
Author(s):  
OU FA ◽  
HE MINGGAO ◽  
WU FUGEN
Keyword(s):  
Second Harmonic ◽  
Optical Nonlinearity ◽  
Photon Absorption ◽  
Saturation Phenomenon ◽  
Sum Frequency ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Threshold Phenomenon ◽  
Anti Stokes ◽  
The Given

A new model to describe the origin of optical nonlinearity is presented. In this model, the interaction between light and medium is reduced to the coupling of photons with phonons, which occurs in the crystal lattice vibrating anharmonically. Then the optical nonlinearity originates from the nonlinear photon–phonon coupling or the interaction among phonons themselves. In this paper, more attention is drawn to the latter. By the given model, (1) degenerate and (2) nondegenerate parametric oscillations, (3) Stokes and (4) anti-Stokes Raman scattering, (5) sum-frequency and (6) second harmonic generation and (7) two-photon absorption are dealt with systematically and quantum-mechanically. The results of theoretical analysis show that the effects (1)–(4) are associated with threshold phenomenon, whereas the effects (5)–(7) with the saturation phenomenon.

Evolution equation for nonlinear Lucassen waves, with application to a threshold phenomenon

2021 ◽  
Vol 150 (5) ◽  
pp. 3648-3663
Author(s):  
Blake E. Simon ◽  
John M. Cormack ◽  
Mark F. Hamilton
Keyword(s):  
Evolution Equation ◽  
Threshold Phenomenon

"Anaerobic threshold": problems of determination and validation

1983 ◽  
Vol 55 (4) ◽  
pp. 1178-1186 ◽  
Author(s):  
M. P. Yeh ◽  
R. M. Gardner ◽  
T. D. Adams ◽  
F. G. Yanowitz ◽  
R. O. Crapo
Keyword(s):  
Anaerobic Threshold ◽  
Stress Test ◽  
Venous Blood ◽  
Test System ◽  
Exercise Tests ◽  
Arterial Lactate ◽  
Blood Samples ◽  
Response Data ◽  
Threshold Phenomenon ◽  
Gas Response

Despite the popularity of the concept of “anaerobic threshold” (AT), the noninvasive detection criteria remain subjective, and invasive validations of AT have been based on lactate data of arterial, mixed venous, venous, and capillary blood samples without any concern for the possible lactate differences from these sources. Eight normal subjects underwent two exercise tests on a bicycle ergometer. The protocol consisted of 3 min of rest, 3 min of 0 work load, and a 20 W/min ramp (1 W/3 s) until exhaustion. Simultaneous arterial and venous blood samples were drawn during the second test. Noninvasive gas response data were measured using a computerized breath-by-breath stress test system. Threshold phenomenon of the lactate accumulation was not found. The arterial lactate levels increased continuously after the start of the exercise ramp. The rise in venous lactate lagged behind the rise of the arterial lactate by about 1.5 min, and therefore venous lactate was not considered suitable for AT detection. Four independent exercise physiologists determined AT from the gas response data. The reviewer variability (avg range 16%) of AT for a given subject was representative of AT values reported for untrained and trained individuals (40-70% maximum O2 consumption). We concluded that 1) AT is not detectable using invasive methods (arterial and venous lactates); and 2) the noninvasive gas response determination has such a large range of reviewer variability that it is unsuitable for clinical use.

scholarly journals Roles of cell and microvillus deformation and receptor-ligand binding kinetics in cell rolling

2008 ◽  
Vol 295 (4) ◽  
pp. H1439-H1450 ◽  
Author(s):  
Parag Pawar ◽  
Sameer Jadhav ◽  
Charles D. Eggleton ◽  
Konstantinos Konstantopoulos
Keyword(s):  
Ligand Binding ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Binding Kinetics ◽  
Cell Deformation ◽  
Receptor Ligand ◽  
Length Scales ◽  
Bond Behavior ◽  
Cell Rolling ◽  
Threshold Phenomenon

Polymorphonuclear leukocyte (PMN) recruitment to sites of inflammation is initiated by selectin-mediated PMN tethering and rolling on activated endothelium under flow. Cell rolling is modulated by bulk cell deformation (mesoscale), microvillus deformability (microscale), and receptor-ligand binding kinetics (nanoscale). Selectin-ligand bonds exhibit a catch-slip bond behavior, and their dissociation is governed not only by the force but also by the force history. Whereas previous theoretical models have studied the significance of these three “length scales” in isolation, how their interplay affects cell rolling has yet to be resolved. We therefore developed a three-dimensional computational model that integrates the aforementioned length scales to delineate their relative contributions to PMN rolling. Our simulations predict that the catch-slip bond behavior and to a lesser extent bulk cell deformation are responsible for the shear threshold phenomenon. Cells bearing deformable rather than rigid microvilli roll slower only at high P-selectin site densities and elevated levels of shear (≥400 s−1). The more compliant cells (membrance stiffness = 1.2 dyn/cm) rolled slower than cells with a membrane stiffness of 3.0 dyn/cm at shear rates >50 s−1. In summary, our model demonstrates that cell rolling over a ligand-coated surface is a highly coordinated process characterized by a complex interplay between forces acting on three distinct length scales.

scholarly journals On the Number of Indecomposable Permutations with a Given Number of Cycles

10.37236/2071 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Robert Cori ◽  
Claire Mathieu ◽  
John Michael Robson
Keyword(s):  
Fixed Ratio ◽  
Threshold Phenomenon ◽  
Asymptotic Probability ◽  
Number Of Cycles

A permutation $a_1a_2\ldots a_n$ is indecomposable if there does not exist $p<n$ such that $a_1a_2\ldots a_p$ is a permutation of $\{ 1,2,\ldots,p\}$. We consider the  probability that a permutation of ${\mathbb S}_n$  with $m$ cycles is indecomposable and prove that  this probability is monotone non-increasing in $n$.We compute  also the asymptotic probability when  $n$ goes to infinity with $m/n$ tending to a fixed ratio.  The asymptotic probability is monotone in $m/n$, and there is no threshold phenomenon: it degrades gracefully from 1 to 0. When $n=2m$, a slight majority ($51.117\ldots$ percent) of the permutations are indecomposable.

Threshold Phenomena and Influence: Perspectives from Mathematics, Computer Science, and Economics

2005 ◽  
Author(s):  
Gil Kalai ◽  
Shmuel Safra
Keyword(s):  
Computer Science ◽  
Political Science ◽  
Monotone Function ◽  
Majority Voting ◽  
Simple Majority ◽  
Condorcet’S Jury Theorem ◽  
Threshold Phenomenon ◽  
Threshold Phenomena ◽  
Aggregation Of Information ◽  
Jury Theorem

Threshold phenomena refer to settings in which the probability for an event to occur changes rapidly as some underlying parameter varies. Threshold phenomena play an important role in probability theory and statistics, physics, and computer science, and are related to issues studied in economics and political science. Quite a few questions that come up naturally in those fields translate to proving that some event indeed exhibits a threshold phenomenon, and then finding the location of the transition and how rapid the change is. The notions of sharp thresholds and phase transitions originated in physics, and many of the mathematical ideas for their study came from mathematical physics. In this chapter, however, we will mainly discuss connections to other fields. A simple yet illuminating example that demonstrates the sharp threshold phenomenon is Condorcet's jury theorem, which can be described as follows. Say one is running an election process, where the results are determined by simple majority, between two candidates, Alice and Bob. If every voter votes for Alice with probability p > 1/2 and for Bob with probability 1 — p, and if the probabilities for each voter to vote either way are independent of the other votes, then as the number of voters tends to infinity the probability of Alice getting elected tends to 1. The probability of Alice getting elected is a monotone function of p, and when there are many voters it rapidly changes from being very close to 0 when p < 1/2 to being very close to 1 when p > 1/2. The reason usually given for the interest of Condorcet's jury theorem to economics and political science [535] is that it can be interpreted as saying that even if agents receive very poor (yet independent) signals, indicating which of two choices is correct, majority voting nevertheless results in the correct decision being taken with high probability, as long as there are enough agents, and the agents vote according to their signal. This is referred to in economics as asymptotically complete aggregation of information.

scholarly journals An Approach to Size Sub-Wavelength Surface Crack Measurements Using Rayleigh Waves Based on Laser Ultrasounds

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5077
Author(s):  
Haiyang Li ◽  
Qianghua Pan ◽  
Xiaotong Zhang ◽  
Zhiwu An
Keyword(s):  
Theoretical Analysis ◽  
Rayleigh Wave ◽  
Surface Crack ◽  
Rayleigh Waves ◽  
Critical Frequency ◽  
Experimental Results ◽  
Notch Depth ◽  
Frequency Method ◽  
Threshold Phenomenon ◽  
Sub Wavelength

In this paper, the interaction of a broadband Rayleigh wave generated by a laser and an artificial rectangular notch is analyzed theoretically and experimentally. For the theoretical analysis, a Gaussian function is adopted to analyze the modulation of notch depth on the frequency spectrum via reflection and transmission coefficients. By the finite element method, the Rayleigh wave generated by pulsed laser beam irradiation and its scattering waves at cracks are calculated. A curve with a slope close to 4 fitted by crack depth and critical wavelength of the threshold phenomenon is obtained by the wavelet transform and Parseval’s theorem according to simulated and experimental results. Based on this relationship, the critical frequency at which the threshold phenomenon happens due to energy transformation of transmission/reflection Rayleigh waves is adopted to determine the size of sub-wavelength surface crack. The experimental results of artificial notch depth estimation on aluminum alloy specimens consistent with theoretical analysis validates the usefulness of the critical frequency method based on a broadband Rayleigh wave generated by laser ultrasonic.

A threshold phenomenon in the propagation of a point source initiated flame

1998 ◽  
Vol 121 (3-4) ◽  
pp. 295-316 ◽  
Author(s):  
Jacques Audounet ◽  
Vincent Giovangigli ◽  
Jean-Michel Roquejoffre
Keyword(s):  
Point Source ◽  
Threshold Phenomenon

Deformation-Induced Lift on Receptor-Ligand Mediated Cell Adhesion to Substrates Explored by a 3-D Computational Fluid Dynamics Approach

2006 ◽  
Author(s):  
Xiaoyi Li ◽  
Kausik Sarkar
Keyword(s):  
Fluid Dynamics ◽  
Cell Deformation ◽  
Dynamics Simulation ◽  
Shear Stresses ◽  
Membrane Elasticity ◽  
Receptor Ligand ◽  
Front Tracking Method ◽  
Threshold Phenomenon ◽  
Surprising Effect ◽  
Downstream Flow

The adhesion of cells to substrates is a critical step in plenty of biological events. The effects of cell deformation on the adhesion process have been investigated using a direct fluid dynamics simulation based on front-tracking method. A model including membrane elasticity and stochastic receptor-ligand binding has been developed. The study reveals a surprising effect of cell deformation. An asymmetry in upstream-downstream flow field due to cell deformation results in a hydrodynamic lift. The lift force counterbalances the shear torque and causes reduced contact area and reduced number of bond formed, and leads to cell detachment at relatively low shear rate. The finding of lift could be used to partially explain the shear threshold phenomenon occurring at small shear stresses.

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