scholarly journals Modular Hamiltonians for the massless Dirac field in the presence of a defect

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Mihail Mintchev ◽  
Erik Tonni
Keyword(s):  
Energy Dissipation ◽  
Ground State ◽  
Initial Point ◽  
Scattering Matrix ◽  
Conjugate Points ◽  
Dirac Field ◽  
Reflection And Transmission ◽  
Point Correlation ◽  
Two Phases ◽  
Local Term

Abstract We study the massless Dirac field on the line in the presence of a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission. Considering this system in its ground state, we derive the modular Hamiltonians of the subregion given by the union of two disjoint equal intervals at the same distance from the defect. The absence of energy dissipation at the defect implies the existence of two phases, where either the vector or the axial symmetry is preserved. Besides a local term, the densities of the modular Hamiltonians contain also a sum of scattering dependent bi-local terms, which involve two conjugate points generated by the reflection and the transmission. The modular flows of each component of the Dirac field mix the trajectory passing through a given initial point with the ones passing through its reflected and transmitted conjugate points. We derive the two-point correlation functions along the modular flows in both phases and show that they satisfy the Kubo-Martin-Schwinger condition. The entanglement entropies are also computed, finding that they do not depend on the scattering matrix.

scholarly journals Modular Hamiltonians for the massless Dirac field in the presence of a boundary

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Mihail Mintchev ◽  
Erik Tonni
Keyword(s):  
Correlation Functions ◽  
Axial Symmetry ◽  
The Other ◽  
Dirac Fermion ◽  
Dirac Field ◽  
General Boundary Conditions ◽  
Point Correlation ◽  
Two Phases ◽  
Local Term ◽  
Massless Dirac Fermion

Abstract We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial symmetry is preserved. In these two phases we derive the corresponding modular Hamiltonian in explicit form. Its density involves a bi-local term localised in two points of the interval, one conjugate to the other. The associated modular flows are also established. Depending on the phase, they mix fields with different chirality or charge that follow different modular trajectories. Accordingly, the modular flow preserves either the vector or the axial symmetry. We compute the two-point correlation functions along the modular flow and show that they satisfy the Kubo-Martin-Schwinger condition in both phases. The entanglement entropies are also derived.

A Family of Efficient Sloshing Liquid Dampers for Suppression of Wind-Induced Instabilities

2003 ◽  
Vol 9 (3-4) ◽  
pp. 361-386 ◽  
Author(s):  
V. J. Modi ◽  
A. Akinturk ◽  
W. Tse
Keyword(s):  
Energy Dissipation ◽  
High Efficiency ◽  
Damping Ratio ◽  
Real Life ◽  
Wind Tunnel Test ◽  
Tall Buildings ◽  
Two Phases ◽  
Liquid Dampers ◽  
Obstacle Geometry ◽  
Floating Particles

Bluff structures in the form of tall buildings, smokestacks, control towers, bridges, etc., are susceptible to vortex resonance and galloping type of instabilities. One approach to vibration control of such systems is through energy dissipation using sloshing liquid dampers. In this paper we focus on enhancing the energy dissipation efficiency of a rectangular liquid damper through the introduction of two-dimensional obstacles as well as floating particles. The investigation has two phases. To begin with, a parametric free vibration study aimed at the optimization of the obstacle geometry is undertaken to arrive at configurations promising increased damping ratio and hence higher energy dissipation. The study is complemented by an extensive wind tunnel test program, which substantiates the effectiveness of this class of damper in suppressing both vortex resonance and galloping type of instabilities. Simplicity of design, ease of implementation, minimal maintenance, reliability as well as high efficiency make such liquid dampers quite attractive for real-life applications.

scholarly journals ARPEC: A NOVEL STAGGERED PERFORATED CAISSON FOR WAVE ABSORPTION AND TIDAL FLUSHING

2020 ◽  
pp. 26
Author(s):  
Paolo Sammarco ◽  
Leopoldo Franco ◽  
Giorgio Bellotti ◽  
Claudia Cecioni ◽  
Stefano DeFinis
Keyword(s):  
Energy Dissipation ◽  
Water Flow ◽  
Wave Energy ◽  
Reflection And Transmission ◽  
Wave Energy Dissipation ◽  
Wave Absorption ◽  
Transmission Coefficients ◽  
Open Sea ◽  
Caisson Breakwater ◽  
Perforated Caisson

An innovative caisson breakwater geometry (patent pending) named "ARPEC" (Anti Reflective PErmeable Caisson) includes openings at all external and internal walls and at lateral (cross) ones, yet in a staggered pattern, to provide a labyrinthian hydraulic communication between the open sea and the internal waters. The complex sinuous water-flow within the consecutive permeable chambers thus favors wave energy dissipation as well as port water flushing and quality, with very low reflection and transmission coefficients. 2D lab model tests demonstrate the system effectiveness.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/PaUsinYO-Zo

scholarly journals WAVE TRANSMISSION THROUGH TRAPEZOIDAL BREAKWATERS

1978 ◽  
Vol 1 (16) ◽  
pp. 129 ◽  
Author(s):  
Ole Secher Madsen ◽  
Paisal Shusang ◽  
Sue Ann Hanson
Keyword(s):  
Energy Dissipation ◽  
Approximate Method ◽  
Cross Section ◽  
Wave Energy ◽  
Graphical Form ◽  
Dissipated Energy ◽  
Simple Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients

In a previous paper Madsen and White (1977) developed an approximate method for the determination of reflection and transmission characteristics of multi-layered, porous rubble-mound breakwaters of trapezoidal cross-section. This approximate method was based on the assumption that the energy dissipation associated with the wave-structure interaction could be considered as two separate mechanisms: (1) an external, frictional dissipation on the seaward slope; (2) an internal dissipation within the porous structure. The external dissipation on the seaward slope was evaluated from the semi-theoretical analysis of energy dissipation on rough, impermeable slopes developed by Madsen and White (1975). The remaining wave energy was represented by an equivalent wave incident on a hydraulically equivalent porous breakwater of rectangular cross-section. The partitioning of the remaining wave energy among reflected, transmitted and internally dissipated energy was evaluated as described by Madsen (1974), leading to a determination of the reflection and transmission coefficients of the structure. The advantage of this previous approximate method was its ease of use. Input data requirements were limited to quantities which would either be known (water depth, wave characteristics, breakwater geometry, and stone sizes) or could be estimated (porosity) by the design engineer. This feature was achieved by the employment of empirical relationships for the parameterization of the external and internal energy dissipation mechanisms. General solutions were presented in graphical form so that calculations could proceed using no more sophisticated equipment than a hand calculator (or a slide rule). This simple method gave estimates of transmission coefficients in excellent agreement with laboratory measurements whereas its ability to predict reflection coefficients left a lot to be desired.

Fracture Toughness of PVC/NBR Blends Evaluated by the J-Integral

1993 ◽  
Vol 66 (4) ◽  
pp. 634-645
Author(s):  
N. Nakajima ◽  
J. L. Liu
Keyword(s):  
Fracture Toughness ◽  
Energy Dissipation ◽  
Crack Initiation ◽  
Crack Tip ◽  
J Integral ◽  
Integral Methods ◽  
Locus Method ◽  
Two Phases ◽  
Fracture Processes

Abstract The effect of gel on the fracture toughness of four PVC/NBR (50/50) blends was characterized by two different J- integral methods. Three of these blends are compatible blends with 33% acrylonitrile in NBRs, and the fourth with 21% acrylonitrile content, is an incompatible blend. Two types of gel are involved in this study microgels and macrogels. The J-integral methods are (1) conventional method proposed by Bagley and Landes and (2) crack initiation locus method proposed by Kim and Joe. The same load-displacement curves are used in both methods. However, the latter eliminates the energy dissipation away from the crack tip in the determination of Jc, while the former does not. Both methods produced almost the same results indicating that the energy dissipation away from the crack tip is negligible in these samples. The fracture toughness of a macrogel-containing blend is much greater than that of a microgel-containing blend, which, in turn, is only slightly greater than that of a gel-free blend. This implies that the two gel-containing blends have different fracture processes. The incompatible blend has the lowest fracture toughness due to weak interaction at the boundaries of the two phases.

scholarly journals Global Minimization of Nonsmooth Constrained Global Optimization with Filled Function

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Wei-xiang Wang ◽  
You-lin Shang ◽  
Ying Zhang
Keyword(s):  
Original Problem ◽  
Initial Point ◽  
Solution Algorithm ◽  
Global Minimization ◽  
Second Phase ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Minimization Problems ◽  
Global Optimizer ◽  
Two Phases

A novel filled function is constructed to locate a global optimizer or an approximate global optimizer of smooth or nonsmooth constrained global minimization problems. The constructed filled function contains only one parameter which can be easily adjusted during the minimization. The theoretical properties of the filled function are discussed and a corresponding solution algorithm is proposed. The solution algorithm comprises two phases: local minimization and filling. The first phase minimizes the original problem and obtains one of its local optimizers, while the second phase minimizes the constructed filled function and identifies a better initial point for the first phase. Some preliminary numerical results are also reported.

Energy dissipation in the ground-state vibrational manifolds ofβ-carotene homologues: A sub-20-fs time-resolved transient grating spectroscopic study

2008 ◽  
Vol 77 (20) ◽  
Author(s):  
Masazumi Fujiwara ◽  
Kensei Yamauchi ◽  
Mitsuru Sugisaki ◽  
Andrew Gall ◽  
Bruno Robert ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Spectroscopic Study ◽  
Ground State ◽  
Transient Grating ◽  
Time Resolved

scholarly journals Identifying a Global Optimizer with Filled Function for Nonlinear Integer Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Wei-Xiang Wang ◽  
You-Lin Shang ◽  
Lian-Sheng Zhang
Keyword(s):  
Integer Programming ◽  
Initial Point ◽  
Local Minimizer ◽  
Nonlinear Integer Programming ◽  
Test Problems ◽  
Integer Programming Problem ◽  
Filled Function ◽  
Global Optimizer ◽  
Filling Phase ◽  
Two Phases

This paper presents a filled function method for finding a global optimizer of integer programming problem. The method contains two phases: the local minimization phase and the filling phase. The goal of the former phase is to identify a local minimizer of the objective function, while the filling phase aims to search for a better initial point for the first phase with the aid of the filled function. A two-parameter filled function is proposed, and its properties are investigated. A corresponding filled function algorithm is established. Numerical experiments on several test problems are performed, and preliminary computational results are reported.

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