1,477 research outputs found
Kinks in dipole chains
It is shown that the topological discrete sine-Gordon system introduced by
Speight and Ward models the dynamics of an infinite uniform chain of electric
dipoles constrained to rotate in a plane containing the chain. Such a chain
admits a novel type of static kink solution which may occupy any position
relative to the spatial lattice and experiences no Peierls-Nabarro barrier.
Consequently the dynamics of a single kink is highly continuum like, despite
the strongly discrete nature of the model. Static multikinks and kink-antikink
pairs are constructed, and it is shown that all such static solutions are
unstable. Exact propagating kinks are sought numerically using the
pseudo-spectral method, but it is found that none exist, except, perhaps, at
very low speed.Comment: Published version. 21 pages, 5 figures. Section 3 completely
re-written. Conclusions unchange
The kink Casimir energy in a lattice sine-Gordon model
The Casimir energy of quantum fluctuations about the classical kink
configuration is computed numerically for a recently proposed lattice
sine-Gordon model. This energy depends periodically on the kink position and is
found to be approximately sinusoidal.Comment: 10 pages, 4 postscript figure
Solar array conceptual design for the Halley's Comet ion drive mission, phase 2
Conceptual design studies were performed directed toward a high power, ultralightweight solar array, compatible with the requirements for the Halley's Comet Ion Drive Mission. A planar, rollup array design concept capable of producing 120 kW at 1 AU and 6 kW at 4.5 AU, and a concentrator, rollup array design concept capable of producing 60 kW at 1 AU and 15.5 kW at 4.5 AU evolved. Both arrays make maximum use of thin film, lightweight technology. The Halley's Comet spacecraft and mission requirements developed from preliminary definition to a more finalized and mature design. As solar array requirements were updated, conceptual design iterations were necessary to keep pace with the rapidly changing program objectives and goals. The Halley's Comet Mission program status and design approaches were reviewed and more realistic power requirements at 4.5 AU for the ion engines were established at the 12 to 16 kW range. This higher power necessitated a change from the planar array design to a concentrator array design in order to remain within suitable cost and weight objectives
The p-weak gradient depends on p
Given \u3b1 > 0, we construct a weighted Lebesgue measure on Rnfor which the family of nonconstant curves has p-modulus zero for p 64 1 + \u3b1 but the weight is a Muckenhoupt Ap weight for p > 1 + \u3b1. In particular, the p-weak gradient is trivial for small p but nontrivial for large p. This answers an open question posed by several authors. We also give a full description of the p-weak gradient for any locally finite Borel measure on R
The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps
The most fruitful approach to studying low energy soliton dynamics in field
theories of Bogomol'nyi type is the geodesic approximation of Manton. In the
case of vortices and monopoles, Stuart has obtained rigorous estimates of the
errors in this approximation, and hence proved that it is valid in the low
speed regime. His method employs energy estimates which rely on a key
coercivity property of the Hessian of the energy functional of the theory under
consideration. In this paper we prove an analogous coercivity property for the
Hessian of the energy functional of a general sigma model with compact K\"ahler
domain and target. We go on to prove a continuity property for our result, and
show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive
in the degree 1 sector. We present numerical evidence which suggests that the
Hessian is globally coercive in a certain equivariance class of the degree n
sector for n>1. We also prove that, within the geodesic approximation, a single
CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded
discussion of the main function spac
Discrete Klein-Gordon models with static kinks free of the Peierls-Nabarro potential
For the nonlinear Klein-Gordon type models, we describe a general method of
discretization in which the static kink can be placed anywhere with respect to
the lattice. These discrete models are therefore free of the {\it static}
Peierls-Nabarro potential. Previously reported models of this type are shown to
belong to a wider class of models derived by means of the proposed method. A
relevant physical consequence of our findings is the existence of a wide class
of discrete Klein-Gordon models where slow kinks {\it practically} do not
experience the action of the Peierls-Nabarro potential. Such kinks are not
trapped by the lattice and they can be accelerated by even weak external
fields.Comment: 6 pages, 2 figure
Translationally invariant nonlinear Schrodinger lattices
Persistence of stationary and traveling single-humped localized solutions in
the spatial discretizations of the nonlinear Schrodinger (NLS) equation is
addressed. The discrete NLS equation with the most general cubic polynomial
function is considered. Constraints on the nonlinear function are found from
the condition that the second-order difference equation for stationary
solutions can be reduced to the first-order difference map. The discrete NLS
equation with such an exceptional nonlinear function is shown to have a
conserved momentum but admits no standard Hamiltonian structure. It is proved
that the reduction to the first-order difference map gives a sufficient
condition for existence of translationally invariant single-humped stationary
solutions and a necessary condition for existence of single-humped traveling
solutions. Other constraints on the nonlinear function are found from the
condition that the differential advance-delay equation for traveling solutions
admits a reduction to an integrable normal form given by a third-order
differential equation. This reduction also gives a necessary condition for
existence of single-humped traveling solutions. The nonlinear function which
admits both reductions defines a two-parameter family of discrete NLS equations
which generalizes the integrable Ablowitz--Ladik lattice.Comment: 24 pages, 4 figure
Recommended from our members
In-line process measurements for injection moulding control. In-line rheology and primary injection phase process measurements for injection moulding of semi-crystalline thermoplastics, using instrumented computer monitored injection moulding machines, for potential use in closed loop process control
In-line rheological and process measurements are studied, during the primary injection
phase, as a potential aid to closed loop process control for injection moulding. The
feasibilities of attaining rheological and process measurements of sufficient accuracy
and precision for use in process control are investigated. The influence of rheological
and process measurements on product quality are investigated for semi-crystalline
thermoplastic materials. A computer based process and machine parameter
monitoring system is utilised to provide accurate and precise process data for analysi
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