scholarly journals Generating a dynamical M2 brane from super-gravitons in a pp-wave background

2021 ◽  
Author(s):  
Jian-Xin Lu
Keyword(s):  
Uncertainty Principle ◽  
Order Parameter ◽  
Critical Phenomenon ◽  
Dynamical Behavior ◽  
Critical Value ◽  
Excess Energy ◽  
The Other ◽  
Single Solution ◽  
Pp Wave ◽  
Size Of Particles

Abstract We present a detail study of dynamically generating a M2 brane from super-gravitons (or D0 branes) in a pp-wave background possessing maximal spacetime SUSY. We have three kinds of dynamical solutions depending on the excess energy which appears as an order parameter signalling a critical phenomenon about the solutions. As the excess energy is below a critical value, we have two branches of the solution, one can have its size zero while the other cannot for each given excess energy. However there can be an instanton tunnelling between the two. Once the excess energy is above the critical value, we have a single solution whose dynamical behavior is basically independent of the background chosen and whose size can be zero at some instant. A by product of this study is that the size of particles or extended objects can grow once there is a non-zero excess energy even without the presence of a background flux, therefore lending support to the spacetime uncertainty principle.

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Dynamical Behavior and Flow Mechanism of Fluid in Nanochannel by Molecular Dynamics Simulation

2009 ◽  
Author(s):  
Juanfang Liu ◽  
Chao Liu ◽  
Qin Li
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Dynamical Behavior ◽  
Velocity Profiles ◽  
The Other ◽  
Dynamics Simulation ◽  
Nonequilibrium Molecular Dynamics ◽  
Interfacial Region ◽  
Flow Mechanism ◽  
Bulk Fluid

The flow properties and dynamical behavior of fluid in a nanochannel were investigated by nonequilibrium molecular dynamics simulation. First of all, the locale distribution of molecules in the channel is found to be strongly inhomogeneous compared to the bulk fluid. In the vicinity of the wall, portion of the fluid molecules are absorbed on the surface of wall due to the strong interaction of the atoms between the wall and liquid, so that the fluid density in the contact region would be much larger than one of the bulk fluid. But in the other region, the local density value approaches one of the bulk fluids with the increasing distance from the wall. This oscillatory behavior of density resulted in different motion behavior of molecules in the different region of nanochannel. The molecular behavior in the interfacial region is remarkably different from those of fluid atoms in the center of channel and wall atoms, which posses both the motion properties of bulk liquids and a solid atom. At the molecular level, macroscopic continuum hypothesis failed, that is, the results predicted by the Navier-Stoke equations deviate from the simulation data adopted by molecular dynamics simulation. In the paper, the velocity profiles for the channels with different width were plotted, which demonstrated that the time-averaged velocity profiles was not quadratic when the channel width was less than 10 molecular diameters. But on the other cases, the velocity profiles will agree well with the analytical solution based on the NS theory. The molecular dynamics simulation method can withdraw the important microscopical information from the simulation process, which benefit to analyze the flow mechanism at such length scale channel.

Comparison of Means: An F Test Followed by a Modified Multiple Range Procedure

1979 ◽  
Vol 4 (1) ◽  
pp. 14-23 ◽  
Author(s):  
Juliet Popper Shaffer
Keyword(s):  
Error Control ◽  
Type I Error ◽  
Critical Value ◽  
The Other ◽  
Type I ◽  
F Test ◽  
Range Test

If used only when a preliminary F test yields significance, the usual multiple range procedures can be modified to increase the probability of detecting differences without changing the control of Type I error. The modification consists of a reduction in the critical value when comparing the largest and smallest means. Equivalence of modified and unmodified procedures in error control is demonstrated. The modified procedure is also compared with the alternative of using the unmodified range test without a preliminary F test, and it is shown that each has advantages over the other under some circumstances.

Extensional flows with viscous heating

2007 ◽  
Vol 571 ◽  
pp. 359-370 ◽  
Author(s):  
JONATHAN J. WYLIE ◽  
HUAXIONG HUANG
Keyword(s):  
Critical Value ◽  
The Other ◽  
Viscous Heating ◽  
Constant Force ◽  
Temperature Dependent ◽  
Downstream Location ◽  
Temperature Dependent Viscosity ◽  
Pulling Forces ◽  
Extensional Flows ◽  
Dependent Viscosity

In this paper we investigate the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. We show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We first consider steady drawing of a thread that is fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling forces above a critical value, we show that inertialess solutions cannot exist and inertia is crucial in controlling the dynamics. We also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension at pinching.

Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

2021 ◽  
pp. 2150002
Author(s):  
Guimin Yang ◽  
Yuanguo Zhu
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Numerical Experiments ◽  
Critical Value ◽  
The Other ◽  
Options Pricing ◽  
Underlying Asset ◽  
Pricing Problems ◽  
Fractional Differential ◽  
The One

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

Dynamical behavior of simplified FitzHugh–Nagumo neural system with time delay driven by Lévy noise

2021 ◽  
pp. 2150240
Author(s):  
Weida Qiu ◽  
Yongfeng Guo ◽  
Xiuxian Yu
Keyword(s):  
Time Delay ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Passage Time ◽  
Neural System ◽  
The Other ◽  
Lévy Noise ◽  
First Passage ◽  
Levy Noise ◽  
System With Time Delay

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

scholarly journals PROPERTIES OF ACCRETION SHOCKS IN VISCOUS FLOWS WITH COOLING EFFECTS

2004 ◽  
Vol 13 (09) ◽  
pp. 1955-1972 ◽  
Author(s):  
SANTABRATA DAS ◽  
SANDIP K. CHAKRABARTI
Keyword(s):  
Shock Wave ◽  
Angular Momentum ◽  
Shock Waves ◽  
Thermodynamic Parameters ◽  
Parameter Space ◽  
Viscous Flows ◽  
Critical Value ◽  
The Other ◽  
Accretion Flows ◽  
Cooling Effects

Low angular momentum accretion flows can have standing and oscillating shock waves. We study the region of the parameter space in which multiple sonic points occur in viscous flows in presence of various cooling effects such as bremsstrahlung and Comptonization. We also quantify the parameter space in which shocks are steady or oscillating. We find that cooling induces effects opposite to heating by viscosity even in modifying the topology of the solutions, though one can never be exactly balanced by the other due to their dissimilar dependence on dynamic and thermodynamic parameters. We show that beyond a critical value of cooling, the flow ceases to contain a shock wave.

Percolation of a random network by statistical physics method

2019 ◽  
Vol 30 (02n03) ◽  
pp. 1950009
Author(s):  
Hai Lin ◽  
Jingcheng Wang
Keyword(s):  
Ising Model ◽  
Cluster Model ◽  
Statistical Physics ◽  
Random Network ◽  
Critical Phenomenon ◽  
Analytical Framework ◽  
Critical Value ◽  
Giant Component ◽  
Random Cluster Model ◽  
Random Cluster

In this paper, we develop an analytical framework and analyze the percolation properties of a random network by introducing statistical physics method. To adequately apply the statistical physics method on the research of a random network, we establish an exact mapping relation between a random network and Ising model. Based on the mapping relation and random cluster model (RCM), we obtain the partition function of the random network and use it to compute the size of the giant component and the critical value of the present probability. We extend this approach to investigate the size of remaining giant component and the critical phenomenon in the random network which is under a certain random attack. Numerical simulations show that our approach is accurate and effective.

Sign in / Sign up

Export Citation Format

Share Document