12,737 research outputs found
The free rigid body dynamics: generalized versus classic
In this paper we analyze the normal forms of a general quadratic Hamiltonian
system defined on the dual of the Lie algebra of real -
skew - symmetric matrices, where is an arbitrary real symmetric
matrix. A consequence of the main results is that any first-order autonomous
three-dimensional differential equation possessing two independent quadratic
constants of motion which admits a positive/negative definite linear
combination, is affinely equivalent to the classical "relaxed" free rigid body
dynamics with linear controls.Comment: 12 page
Illinois Waterfowl Harvest, Hunter Activity, and Attitudes Toward September Canada Goose Season, Canada Goose Harvest Monitoring System, and Dates for Hunting Seasons, 1997-98
The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems
We present a new variational principle for the gyrokinetic system, similar to
the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in
the Eulerian frame and based on constrained variations of the phase space fluid
velocity and particle distribution function. Using a Legendre transform, we
explicitly derive the field theoretic Hamiltonian structure of the system. This
is carried out with a modified Dirac theory of constraints, which is used to
construct meaningful brackets from those obtained directly from
Euler-Poincar\'{e} theory. Possible applications of these formulations include
continuum geometric integration techniques, large-eddy simulation models and
Casimir type stability methods.
[1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur
Continuous and discrete Clebsch variational principles
The Clebsch method provides a unifying approach for deriving variational
principles for continuous and discrete dynamical systems where elements of a
vector space are used to control dynamics on the cotangent bundle of a Lie
group \emph{via} a velocity map. This paper proves a reduction theorem which
states that the canonical variables on the Lie group can be eliminated, if and
only if the velocity map is a Lie algebra action, thereby producing the
Euler-Poincar\'e (EP) equation for the vector space variables. In this case,
the map from the canonical variables on the Lie group to the vector space is
the standard momentum map defined using the diamond operator. We apply the
Clebsch method in examples of the rotating rigid body and the incompressible
Euler equations. Along the way, we explain how singular solutions of the EP
equation for the diffeomorphism group (EPDiff) arise as momentum maps in the
Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch
variational principle is discretised to produce a variational integrator for
the dynamical system. We obtain a discrete map from which the variables on the
cotangent bundle of a Lie group may be eliminated to produce a discrete EP
equation for elements of the vector space. We give an integrator for the
rotating rigid body as an example. We also briefly discuss how to discretise
infinite-dimensional Clebsch systems, so as to produce conservative numerical
methods for fluid dynamics
Spatiotemporal patterns and agro-ecological risk factors for cutaneous and renal glomerular vasculopathy (Alabama Rot) in dogs in the UK
Seasonal outbreaks of cutaneous and renal glomerular vasculopathy (CRGV) have been reported annually in UK dogs since 2012, yet the aetiology of the disease remains unknown. The objectives of this study were to explore whether any breeds had an increased or decreased risk of being diagnosed with CRGV, and to report on age and sex distributions of CRGV cases occurring in the UK. Multivariable logistic regression was used to compare 101 dogs diagnosed with CRGV between November 2012 and May 2017 with a denominator population of 446,453 dogs from the VetCompass database. Two Kennel Club breed groups—hounds (odds ratio (OR) 10.68) and gun dogs (OR 9.69)—had the highest risk of being diagnosed with CRGV compared with terriers, while toy dogs were absent from among CRGV cases. Females were more likely to be diagnosed with CRGV (OR 1.51) as were neutered dogs (OR 3.36). As well as helping veterinarians develop an index of suspicion for the disease, better understanding of the signalment risk factors may assist in the development of causal models for CRGV and help identify the aetiology of the disease
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
Theory and simulations of rigid polyelectrolytes
We present theoretical and numerical studies on stiff, linear
polyelectrolytes within the framework of the cell model. We first review
analytical results obtained on a mean-field Poisson-Boltzmann level, and then
use molecular dynamics simulations to show, under which circumstances these
fail quantitatively and qualitatively. For the hexagonally packed nematic phase
of the polyelectrolytes we compute the osmotic coefficient as a function of
density. In the presence of multivalent counterions it can become negative,
leading to effective attractions. We show that this results from a reduced
contribution of the virial part to the pressure. We compute the osmotic
coefficient and ionic distribution functions from Poisson-Boltzmann theory with
and without a recently proposed correlation correction, and also simulation
results for the case of poly(para-phenylene) and compare it to recently
obtained experimental data on this stiff polyelectrolyte. We also investigate
ion-ion correlations in the strong coupling regime, and compare them to
predictions of the recently advocated Wigner crystal theories.Comment: 32 pages, 15 figures, proceedings of the ASTATPHYS-MEX-2001, to be
published in Mol. Phy
Fast Dynamic Graph Algorithms for Parameterized Problems
Fully dynamic graph is a data structure that (1) supports edge insertions and
deletions and (2) answers problem specific queries. The time complexity of (1)
and (2) are referred to as the update time and the query time respectively.
There are many researches on dynamic graphs whose update time and query time
are , that is, sublinear in the graph size. However, almost all such
researches are for problems in P. In this paper, we investigate dynamic graphs
for NP-hard problems exploiting the notion of fixed parameter tractability
(FPT).
We give dynamic graphs for Vertex Cover and Cluster Vertex Deletion
parameterized by the solution size . These dynamic graphs achieve almost the
best possible update time and the query time
, where is the time complexity of any static
graph algorithm for the problems. We obtain these results by dynamically
maintaining an approximate solution which can be used to construct a small
problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a
corollary, we obtain a quasilinear-time (polynomial) kernelization algorithm
for Cluster Vertex Deletion. Until now, only quadratic time kernelization
algorithms are known for this problem.
We also give a dynamic graph for Chromatic Number parameterized by the
solution size of Cluster Vertex Deletion, and a dynamic graph for
bounded-degree Feedback Vertex Set parameterized by the solution size. Assuming
the parameter is a constant, each dynamic graph can be updated in
time and can compute a solution in time. These results are obtained by
another approach.Comment: SWAT 2014 to appea
Signalment risk factors for cutaneous and renal glomerular vasculopathy (Alabama rot) in dogs in the UK
Seasonal outbreaks of cutaneous and renal glomerular vasculopathy (CRGV) have been reported annually in UK dogs since 2012, yet the aetiology of the disease remains unknown. The objectives of this study were to explore whether any breeds had an increased or decreased risk of being diagnosed with CRGV, and to report on age and sex distributions of CRGV cases occurring in the UK. Multivariable logistic regression was used to compare 101 dogs diagnosed with CRGV between November 2012 and May 2017 with a denominator population of 446,453 dogs from the VetCompass database. Two Kennel Club breed groups—hounds (odds ratio (OR) 10.68) and gun dogs (OR 9.69)—had the highest risk of being diagnosed with CRGV compared with terriers, while toy dogs were absent from among CRGV cases. Females were more likely to be diagnosed with CRGV (OR 1.51) as were neutered dogs (OR 3.36). As well as helping veterinarians develop an index of suspicion for the disease, better understanding of the signalment risk factors may assist in the development of causal models for CRGV and help identify the aetiology of the disease
Optimizing the third-and-a-half post-Newtonian gravitational radiation-reaction force for numerical simulations
The gravitational radiation-reaction force acting on perfect fluids at 3.5
post-Newtonian order is cast into a form which is directly applicable to
numerical simulations. Extensive use is made of metric-coefficient changes
induced by functional coordinate transformations, of the continuity equation,
as well as of the equations of motion. We also present an expression
appropriate for numerical simulations of the radiation field causing the worked
out reaction force.Comment: 22 pages to appear in Physical Review
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