scholarly journals Scale-invariant singularity of the surface quasigeostrophic patch

2019 ◽  
Vol 863 ◽  
Author(s):  
R. K. Scott ◽  
D. G. Dritschel
Keyword(s):  
Numerical Simulations ◽  
Finite Time ◽  
Initial Conditions ◽  
Logarithmic Spiral ◽  
Analytic Form ◽  
Scale Invariant ◽  
Boundary Curvature ◽  
Simple Analytic Form

Numerical simulations of the surface quasigeostrophic patch indicate the development of a scale-invariant singularity of the boundary curvature in finite time, with some evidence of universality across a variety of initial conditions. At the time of singularity, boundary segments are shown to possess an exact and simple analytic form, described by branches of a logarithmic spiral centred on the point of singularity. The angles between the branches depend non-trivially on the shape of the smooth connecting boundary as the singularity is approached, but are independent of the global boundary.

scholarly journals Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongbin Wang ◽  
Binhua Feng
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Critical Case ◽  
Blow Up ◽  
Critical Mass ◽  
Choquard Equation ◽  
Power Type ◽  
Scale Invariant ◽  
Nonlinear Schrödinger ◽  
Sharp Thresholds

AbstractIn this paper, we consider the sharp thresholds of blow-up and global existence for the nonlinear Schrödinger–Choquard equation $$ i\psi _{t}+\Delta \psi =\lambda _{1} \vert \psi \vert ^{p_{1}}\psi +\lambda _{2}\bigl(I _{\alpha } \ast \vert \psi \vert ^{p_{2}}\bigr) \vert \psi \vert ^{p_{2}-2}\psi . $$iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. We derive some finite time blow-up results. Due to the failure of this equation to be scale invariant, we obtain some sharp thresholds of blow-up and global existence by constructing some new estimates. In particular, we prove the global existence for this equation with critical mass in the $L^{2}$L2-critical case. Our obtained results extend and improve some recent results.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

Theory of the stabilization of colloids by adsorbed polymer

1974 ◽  
Vol 337 (1611) ◽  
pp. 509-516 ◽  
Keyword(s):  
Plane Surface ◽  
Analytic Form ◽  
Polymer Chains ◽  
Contour Length ◽  
Link Length ◽  
Excluded Volume Effects ◽  
Adsorbed Polymer ◽  
Random Flight ◽  
The Stability ◽  
Simple Analytic Form

The configurational free energy of random flight polymer chains adsorbed by one end onto a plane surface as a function of the distance from a parallel plane surface is expressed to a good approximation in simple analytic form. The result is used to discuss the stabilization of a colloid suspension by adsorbed polymer. According to this theory two types of aggregation of colloid particles may occur. If LI < AS/2π 3 NkT , where l is the link length and L the contour length of a polymer chain, A is the Hamaker constant, N /S is the number of adsorbed polymer chains per unit area and kT is the Boltzman constant multiplied by temperature, the particles adhere closely, but if AS/2π 3 kT < IL < AS/nkT lg 2N a looser association is formed. It is expected that the presence of excluded volume effects would greatly increase the stability against the looser association.

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

Stochastic storage networks: stationarity and the feedforward case

1997 ◽  
Vol 34 (02) ◽  
pp. 498-507 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Total Variation ◽  
Finite Time ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Input Process ◽  
Stationary Increments ◽  
Stationary Version ◽  
Storage Network ◽  
The Difference ◽  
Storage Networks

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

Why Is Climate Sensitivity So Unpredictable?

Science ◽  
2007 ◽  
Vol 318 (5850) ◽  
pp. 629-632 ◽  
Author(s):  
Gerard H. Roe ◽  
Marcia B. Baker
Keyword(s):  
Climate Change ◽  
Atmospheric Carbon Dioxide ◽  
Probability Distributions ◽  
Analytic Form ◽  
Future Climate Change ◽  
Large Temperature ◽  
Global Mean Temperature ◽  
Simple Analytic Form ◽  
Global Mean

Uncertainties in projections of future climate change have not lessened substantially in past decades. Both models and observations yield broad probability distributions for long-term increases in global mean temperature expected from the doubling of atmospheric carbon dioxide, with small but finite probabilities of very large increases. We show that the shape of these probability distributions is an inevitable and general consequence of the nature of the climate system, and we derive a simple analytic form for the shape that fits recent published distributions very well. We show that the breadth of the distribution and, in particular, the probability of large temperature increases are relatively insensitive to decreases in uncertainties associated with the underlying climate processes.

Boundary-layer-induced potential flow on an elliptic cylinder

1974 ◽  
Vol 66 (1) ◽  
pp. 145-157 ◽  
Author(s):  
Stanley G. Rubin ◽  
Frank J. Mummolo
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elliptic Cylinder ◽  
Analytic Form ◽  
Slender Body ◽  
Dimensional Solution ◽  
Slender Body Theory ◽  
Simple Analytic Form ◽  
Body Theory

The application of slender-body theory to the evaluation of the three-dimensional surface velocities induced by a boundary layer on an elliptic cylinder is considered. The method is applicable when the Reynolds number is sufficiently large so that the thin-boundary-layer approximation is valid. The resulting potential problem is reduced to a two-dimensional consideration of the flow over an expanding cylinder with porous boundary conditions. The limiting solutions for a flat plate of finite span and a nearly circular cross-section are obtained in a simple analytic form. In the former case, within the limitations of slender-body theory, the results are in exact agreement with the complete three-dimensional solution for this geometry.

Evaluation of Cumulative Damage From Drop to Puncture Conditions

2012 ◽  
Author(s):  
Woo-Seok Choi ◽  
Sanghoon Lee ◽  
Kyoung-Sik Bang ◽  
Ju-Chan Lee ◽  
Ki-Seog Seo
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Water Immersion ◽  
Cumulative Damage ◽  
Single Event ◽  
Physical Test ◽  
Sequential Event ◽  
Physical Tests ◽  
Hypothetical Accident ◽  
Accident Conditions

During safety assessments of transport packages, cumulative damages are naturally accumulated for assessments performed using physical tests specimens. However, the cumulative damages are not as easily accounted when assessments are by numerical simulations. While analysts are comfortable with simulating packages for single events, it is not yet common practice to incorporate the effect handed over from a former event to the next, in a series of sequential load events. Thus, many numerical simulations in SAR (Safety Analysis Report) represent just a single event in the series of sequential event comprising the required accident condition. These single event numerical simulations are then based on initial conditions different from the analogous physical test specimen, which could contribute to a growing disparity in results between assessments by physically testing compared to numerical simulation. The reason why analyses do not consider the cumulative damage is difficulties in delivering the final result of the previous analysis to the current analysis. The hypothetical accident conditions described in the IAEA regulations include drop, puncture, fire, and water immersion conditions, which should be sequentially simulated. There can be cumulative damage between two accident conditions, such as drop and puncture, puncture and fire, and so forth. In this study, as the first step to consider cumulative damage, an analysis technology to perform a puncture analysis incorporating the final response field from a prior drop analysis is proposed. The necessity and validity of the proposed analysis technology are evaluated by a comparison with the results obtained by performing each analysis independently.

scholarly journals Broadband Microwave Absorption by Logarithmic Spiral Metasurface

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Shubo Wang ◽  
Bo Hou ◽  
Che Ting Chan
Keyword(s):  
Electromagnetic Wave ◽  
Scale Invariance ◽  
Logarithmic Spiral ◽  
Unit Cell ◽  
Scale Invariant ◽  
Archimedean Spiral ◽  
Broadband Absorption ◽  
Fabry Perot ◽  
Classical Waves

Abstract Metamaterials have enabled the design of electromagnetic wave absorbers with unprecedented performance. Conventional metamaterial absorbers usually employ multiple structure components in one unit cell to achieve broadband absorption. Here, a simple metasurface microwave absorber is proposed that has one metal-backed logarithmic spiral resonator as the unit cell. It can absorb >95% of normally incident microwave energy within the frequency range of 6 GHz–37 GHz as a result of the scale invariant geometry and the Fabry-Perot-type resonances of the resonator. The thickness of the metasurface is 5 mm and approaches the Rozanov limit of an optimal absorber. The physics underlying the broadband absorption is discussed. A comparison with Archimedean spiral metasurface is conducted to uncover the crucial role of scale invariance. The study opens a new direction of electromagnetic wave absorption by employing the scale invariance of Maxwell equations and may also be applied to the absorption of other classical waves such as sound.

scholarly journals Finite-Time Synchronization of Complex Dynamical Networks with Nondelayed and Delayed Coupling by Continuous Function Controller

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xie Chengrong ◽  
Xing Yu ◽  
Xia Qing ◽  
Dongbing Tong ◽  
Yuhua Xu
Keyword(s):  
Continuous Function ◽  
Numerical Simulations ◽  
Finite Time ◽  
Time Synchronization ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Delayed Coupling ◽  
Special Case

This paper investigates the finite-time synchronization of complex dynamical networks with nondelayed and delayed coupling. By designing a simple continuous function controller, sufficient criteria for finite-time synchronization of dynamical networks with nondelayed and delayed coupling are obtained. As a special case, the continuous function controller designed in this paper may be the simplest and easy to implement for the finite-time synchronization of dynamical networks without delay. Finally, numerical simulations are given to verify the effectiveness of the conclusions presented in this paper.

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