scholarly journals Eigenstates and Eigenvalues of Chain Hamiltonians Based on Multiparameter Braid Matrices for All Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
B. Abdesselam ◽  
A. Chakrabarti
Keyword(s):  
Boundary Conditions ◽  
Energy Levels ◽  
Circular Boundary ◽  
Explicit Constructions ◽  
Free Parameters ◽  
Chain Lengths

We study chain Hamiltonians derived from a class of multidimensional, multiparameter braid matrices introduced and explored in a series of previous papers. The N2 × N2 braid matrices (for all N) have 1/2N2 free parameters for even N and 1/2N+12-1 for N odd. We present systematic explicit constructions for eigenstates and eigenvalues of chain Hamiltonians for N=2,3,4 and all chain lengths r. We derive explicitly the constraints imposed on these states by periodic (circular) boundary conditions. Our results thus cover both open and closed chains. We then indicate how our formalism can be extended for all N,r. The dependence of the eigenvalues on the free parameters is displayed explicitly, showing how the energy levels and their differences vary in a particular simple way with these parameters. Some perspectives are discussed in conclusion.

Simulations of electric field at the initiation altitudes of sprites and halos generated by the thundercloud charge structure and lightning channels of causative return strokes

2021 ◽  
Author(s):  
Petr Kaspar ◽  
Ivana Kolmasova ◽  
Ondrej Santolik ◽  
Martin Popek ◽  
Pavel Spurny ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Electric Field ◽  
Boundary Conditions ◽  
Free Space ◽  
Nonlinear Effects ◽  
Charge Structure ◽  
Transient Luminous Events ◽  
Lightning Channel ◽  
Free Parameters

<p><span>Sprites and halos are transient luminous events occurring above thunderclouds. They can be observed simultaneously or they can also appear individually. Circumstances leading to initiation of these events are still not completely understood. In order to clarify the role of lightning channels of causative lightning return strokes and the corresponding thundercloud charge structure, we have developed a new model of electric field amplitudes at halo/sprite altitudes. It consists of electrostatic and inductive components of the electromagnetic field generated by the lightning channel in free space at a height of 15 km. Above this altitude we solve Maxwell’s equations self-consistently including the nonlinear effects of heating and ionization/attachment of the electrons. At the same time, we investigate the role of a development of the thundercloud charge structure and related induced charges above the thundercloud. We show how these charges lead to the different distributions of the electric field at the initiation heights of the halos and sprites. We adjust free parameters of the model using observations of halos and sprites at the Nydek TLE observatory and using measurements of luminosity curves of the corresponding return strokes measured by an array of fast photometers. The latter measurements are also used to set the boundary conditions of the model.</span></p>

Standard Chain Lever Load Binder

2012 ◽  
Author(s):  
Ralph L. Barnett ◽  
Theodore Liber
Keyword(s):  
Boundary Conditions ◽  
Energy Levels ◽  
Product Liability ◽  
Lateral Force ◽  
Complete Analysis ◽  
Safety Hazards ◽  
Force Components ◽  
Cable Forces ◽  
The Cost ◽  
Alternative Designs

The standard chain lever load binder that is used for truck cargo securement operates on an over-center principle that has been used for over a century on suitcases, tool boxes and camera cases. The safety hazards associated with the uses and misuses of the load binder were identified decades ago and various inventors patented innovations that eliminated or mitigated the safety shortcomings. Furthermore, their ideas were not only effective, they were economical, versatile, and efficient. These patents are now in the public domain and many companies manufacture and/or distribute entire lines of securement that include not only the standard chain lever load binder but most of the alternative designs as well. This case study takes the position that the standard chain lever load binder should be banished. Since the appropriate bodies, after all these years, have not arranged for its demise, this paper appeals to the product liability system for safety relief. Engineering analysis and tests are provided to the legal profession to help them protect us by making the cost advantage of the standard binder too expensive. This paper explores some of the remarkable properties of the standard load binder, e.g., • Load binders develop very large chain tensions and very high levels of recoverable energy. The standard chain lever load binder does not enable the tension and energy levels to be safely maintained or released. • The handle slack on the standard load binder cannot be fine-tuned; consequently, a scenario is frequently encountered where the chain is either too loose or too tight to secure with the binder handle. This is the major motivation for resorting to a “cheater bar.” • A complete analysis of the securement forces acting on the cargo and load binder is seldom possible because the system is a “moving target.” The handle loading is randomly applied by human exertion which changes with handle orientation. The boundary conditions depend not only on the cargo and securement strategy, but on the loading itself. Unknown friction characteristics of the loading affect the distribution of chain forces. • On one side of the load binder the chain tension can always be predicted using only the handle torque. This cable tension is independent of the boundary conditions and any axial handle force components. • When the load binder system is rigid, it gives rise to three singularities. The mechanical advantage is unbounded at the two extreme handle orientations. When the binder is suspended in a taut condition, any lateral force on the binder develops infinite cable forces. • Handle slack has a profound effect on the handle resistance, the resilience, the chain tension, and the latching capability.

ADIABATIC TRANSPORT PROPERTIES AND BERRY’S PHASE IN HEISENBERG-ISING RING

1991 ◽  
Vol 05 (03) ◽  
pp. 497-507 ◽  
Author(s):  
V.E. KOREPIN ◽  
A.C.T. WU
Keyword(s):  
Boundary Conditions ◽  
Transport Properties ◽  
Effective Charge ◽  
Spin Chain ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

In a recent paper, B. Sutherland and B.S. Shastry have constructed an adiabatic process for the Heisenberg spin chain (spin ½) with respect to a change of boundary conditions. In this paper we calculate Berry’s phase for this process. We also evaluate the dependence of energy levels on boundary conditions which permits us to calculate the effective charge-carrying mass.

scholarly journals GLOBAL THEORY OF QUANTUM BOUNDARY CONDITIONS AND TOPOLOGY CHANGE

2005 ◽  
Vol 20 (05) ◽  
pp. 1001-1025 ◽  
Author(s):  
M. ASOREY ◽  
A. IBORT ◽  
G. MARMO
Keyword(s):  
Boundary Conditions ◽  
Boundary Data ◽  
Energy Levels ◽  
Cayley Transform ◽  
Edge States ◽  
Topology Change ◽  
Global Theory ◽  
Relevant Role ◽  
Quantum Boundary Conditions ◽  
Low Dimensional

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold M with regular boundary Γ=∂M. The space ℳ of self-adjoint extensions of the covariant Laplacian on M is shown to have interesting geometrical and topological properties which are related to the different topological closures of M. In this sense, the change of topology of M is connected with the nontrivial structure of ℳ. The space ℳ itself can be identified with the unitary group [Formula: see text] of the Hilbert space of boundary data [Formula: see text]. This description, is shown to be equivalent to the classical von Neumann's description in terms of deficiency index subspaces, but it is more efficient and explicit because it is given only in terms of the boundary data, which are the natural external inputs of the system. A particularly interesting family of boundary conditions, identified as the set of unitary operators which are singular under the Cayley transform, [Formula: see text] (the Cayley manifold), turns out to play a relevant role in topology change phenomena. The singularity of the Cayley transform implies that some energy levels, usually associated with edge states, acquire an infinity energy when by an adiabatic change the boundary conditions reaches the Cayley submanifold 𝒞_. In this sense topological transitions require an infinite amount of quantum energy to occur, although the description of the topological transition in the space ℳ is smooth. This fact has relevant implications in string theory for possible scenarios with joint descriptions of open and closed strings. In the particular case of elliptic self-adjoint boundary conditions, the space 𝒞_ can be identified with a Lagrangian submanifold of the infinite dimensional Grassmannian. The corresponding Cayley manifold 𝒞_ is dual of the Maslov class of ℳ. The phenomena are illustrated with some simple low dimensional examples.

scholarly journals Energy levels of ABC-stacked trilayer graphene quantum dots with infinite-mass boundary conditions

2016 ◽  
Vol 94 (16) ◽  
Author(s):  
M. Mirzakhani ◽  
M. Zarenia ◽  
D. R. da Costa ◽  
S. A. Ketabi ◽  
F. M. Peeters
Keyword(s):  
Quantum Dots ◽  
Boundary Conditions ◽  
Energy Levels ◽  
Graphene Quantum Dots ◽  
Infinite Mass ◽  
Trilayer Graphene ◽  
Infinite Mass Boundary Conditions

scholarly journals Maxwell-Chern-Simons Casimir effect. II. Circular boundary conditions

1992 ◽  
Vol 46 (2) ◽  
pp. 842-852 ◽  
Author(s):  
Kimball A. Milton ◽  
Y. Jack Ng
Keyword(s):  
Boundary Conditions ◽  
Casimir Effect ◽  
Circular Boundary ◽  
Chern Simons

A stochastic theory of community food webs. III. Predicted and observed lengths of food chains

1986 ◽  
Vol 228 (1252) ◽  
pp. 317-353 ◽  
Keyword(s):  
Food Webs ◽  
Goodness Of Fit ◽  
Scaling Law ◽  
Stochastic Theory ◽  
Exact Formula ◽  
Cascade Model ◽  
Food Chains ◽  
Expected Number ◽  
Free Parameters ◽  
Chain Lengths

This paper offers a quantitative theory of the length of food chains. The theory derives from a mathematical model of community food webs called the cascade model. The paper tests the predictions against data from real webs. An exact formula for the expected number of chains of each length in a model web with any given finite number, S , of species is, to our knowledge, the first exactly derived theory of the length of food chains. Since the numbers of chains of different lengths are dependent in the cascade model, we evaluate the goodness of fit between the observed and predicted numbers of chains by a Monte Carlo method. Without fitting any free parameters, and using no direct information about chain lengths other than that implied by the total number of species and the total number of links in a web, we find that the cascade model describes acceptably the observed numbers of chains of each length in all but 16 or 17 of 113 webs. Of 62 webs previously used to test the cascade model, the cascade model describes acceptably the chain lengths in all but 11 or 12. With a fresh batch of 51 webs, we establish first that (apart from two outlying webs) the numbers of links are very nearly proportional to the numbers of species and that the constant of proportionality is consistent with that in the original 62 webs. This finding verifies the so-called species–link scaling law with new data. The cascade model describes acceptably the chain lengths of all but 5 of the 51 new webs. Most of the 16 or 17 webs with chain lengths described poorly by the cascade model have unusually large average chain lengths (greater than 4 links) or unusually small average chain lengths (fewer than 2 links).

The Effect of the Boundary Conditions on the Impact Behaviors of Stitched Composite Lap Joints

2016 ◽  
Vol 25 (1) ◽  
pp. 096369351602500
Author(s):  
Emin Ergun ◽  
Ismail Gökkaya
Keyword(s):  
Boundary Conditions ◽  
Energy Levels ◽  
Composite Plates ◽  
Lap Joints ◽  
Transverse Impact ◽  
Adhesively Bonded ◽  
Bonded Composite ◽  
Infusion Method ◽  
Impact Characteristics ◽  
The Impact

In this study, transverse impact behaviors of stitch adhesively bonded composite lap joints having three different overlap lengths (20, 40 and 60 mm) at different energy levels are investigated. The effects of the boundary conditions (clamped-clamped and clamped-free) and three different span lengths (40, 60 and 80 mm) have been determined. The impacts energies are varied in a range from 5 J to 20 J. Vacuum assisted resin infusion method (VARIM) is used to manufacture composite plates. It is shown that the boundary conditions and span lengths affect considerably the impact responses of the stitch composites lap joints. The important impact characteristics of the composite lap joints are compared with each other and discussed. The observed damages of the composite lap joints are presented.

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