903 research outputs found
Qualitative Criterion for Interception in a Pursuit/Evasion Game
A qualitative account is given of a differential pursuit/evasion game. A
criterion for the existence of an intercept solution is obtained using future
cones that contain all attainable trajectories of target or interceptor
originating from an initial position. A sufficient and necessary conditon that
an opportunity to intercept always exist is that, after some initial time, the
future cone of the target be contained within the future cone of the
interceptor. The sufficient condition may be regarded as a kind of Nash
equillibrium.Comment: 8 pages; revsions and corrigend
Markov Process of Muscle Motors
We study a Markov random process describing a muscle molecular motor
behavior. Every motor is either bound up with a thin filament or unbound. In
the bound state the motor creates a force proportional to its displacement from
the neutral position. In both states the motor spend an exponential time
depending on the state. The thin filament moves at its velocity proportional to
average of all displacements of all motors. We assume that the time which a
motor stays at the bound state does not depend on its displacement. Then one
can find an exact solution of a non-linear equation appearing in the limit of
infinite number of the motors.Comment: 10 page
General solution of equations of motion for a classical particle in 9-dimensional Finslerian space
A Lagrangian description of a classical particle in a 9-dimensional flat
Finslerian space with a cubic metric function is constructed. The general
solution of equations of motion for such a particle is obtained. The Galilean
law of inertia for the Finslerian space is confirmed.Comment: 10 pages, LaTeX-2e, no figures; added 2 reference
Topological surface states in three-dimensional magnetic insulators
An electron moving in a magnetically ordered background feels an effective
magnetic field that can be both stronger and more rapidly varying than typical
externally applied fields. One consequence is that insulating magnetic
materials in three dimensions can have topologically nontrivial properties of
the effective band structure. For the simplest case of two bands, these "Hopf
insulators" are characterized by a topological invariant as in quantum Hall
states and Z_2 topological insulators, but instead of a Chern number or parity,
the underlying invariant is the Hopf invariant that classifies maps from the
3-sphere to the 2-sphere. This paper gives an efficient algorithm to compute
whether a given magnetic band structure has nontrivial Hopf invariant, a
double-exchange-like tight-binding model that realizes the nontrivial case, and
a numerical study of the surface states of this model.Comment: 4 pages, 2 figures; published versio
Composite Dipolar Recoupling: Anisotropy Compensated Coherence Transfer in Solid-State NMR
The efficiency of dipole-dipole coupling driven coherence transfer
experiments in solid-state NMR spectroscopy of powder samples is limited by
dispersion of the orientation of the internuclear vectors relative to the
external magnetic field. Here we introduce general design principles and
resulting pulse sequences that approach full polarization transfer efficiency
for all crystallite orientations in a powder in magic-angle-spinning
experiments. The methods compensate for the defocusing of coherence due to
orientation dependent dipolar coupling interactions and inhomogeneous
radio-frequency fields. The compensation scheme is very simple to implement as
a scaffold (comb) of compensating pulses in which the pulse sequence to be
improved may be inserted. The degree of compensation can be adjusted and should
be balanced as a compromise between efficiency and length of the overall pulse
sequence. We show by numerical and experimental data that the presented
compensation protocol significantly improves the efficiency of known dipolar
recoupling solid-state NMR experiment
A linear theory for control of non-linear stochastic systems
We address the role of noise and the issue of efficient computation in
stochastic optimal control problems. We consider a class of non-linear control
problems that can be formulated as a path integral and where the noise plays
the role of temperature. The path integral displays symmetry breaking and there
exist a critical noise value that separates regimes where optimal control
yields qualitatively different solutions. The path integral can be computed
efficiently by Monte Carlo integration or by Laplace approximation, and can
therefore be used to solve high dimensional stochastic control problems.Comment: 5 pages, 3 figures. Accepted to PR
First passage times and asymmetry of DNA translocation
Motivated by experiments in which single-stranded DNA with a short hairpin
loop at one end undergoes unforced diffusion through a narrow pore, we study
the first passage times for a particle, executing one-dimensional brownian
motion in an asymmetric sawtooth potential, to exit one of the boundaries. We
consider the first passage times for the case of classical diffusion,
characterized by a mean-square displacement of the form , and for the case of anomalous diffusion or subdiffusion, characterized by a
mean-square displacement of the form with
. In the context of classical diffusion, we obtain an expression
for the mean first passage time and show that this quantity changes when the
direction of the sawtooth is reversed or, equivalently, when the reflecting and
absorbing boundaries are exchanged. We discuss at which numbers of `teeth'
(or number of DNA nucleotides) and at which heights of the sawtooth potential
this difference becomes significant. For large , it is well known that the
mean first passage time scales as . In the context of subdiffusion, the
mean first passage time does not exist. Therefore we obtain instead the
distribution of first passage times in the limit of long times. We show that
the prefactor in the power relation for this distribution is simply the
expression for the mean first passage time in classical diffusion. We also
describe a hypothetical experiment to calculate the average of the first
passage times for a fraction of passage events that each end within some time
. We show that this average first passage time scales as in
subdiffusion.Comment: 10 pages, 4 figures We incorporated reviewers' suggestions from
Physical Review E. We reformulated a few paragraphs in the introduction and
further clarified the issue of the (a)symmetry of passage times. In the
results section, we re-expressed the results in a form that manifest the
important features. We also added a few references concerning anomalous
diffusion. The look (but not the content) of figure 1 was also change
Partial order and a -topology in a set of finite quantum systems
A `whole-part' theory is developed for a set of finite quantum systems
with variables in . The partial order `subsystem'
is defined, by embedding various attributes of the system (quantum
states, density matrices, etc) into their counterparts in the supersystem
(for ). The compatibility of these embeddings is studied. The
concept of ubiquity is introduced for quantities which fit with this structure.
It is shown that various entropic quantities are ubiquitous. The sets of
various quantities become -topological spaces with the divisor topology,
which encapsulates fundamental physical properties. These sets can be converted
into directed-complete partial orders (dcpo), by adding `top elements'. The
continuity of various maps among these sets is studied
Universal Approach to Optimal Photon Storage in Atomic Media
We present a universal physical picture for describing storage and retrieval
of photon wave packets in a Lambda-type atomic medium. This physical picture
encompasses a variety of different approaches to pulse storage ranging from
adiabatic reduction of the photon group velocity and pulse-propagation control
via off-resonant Raman fields to photon-echo based techniques. Furthermore, we
derive an optimal control strategy for storage and retrieval of a photon wave
packet of any given shape. All these approaches, when optimized, yield
identical maximum efficiencies, which only depend on the optical depth of the
medium.Comment: 4 pages, 3 figures. V2: major changes in presentation (title,
abstract, main text), simplification of derivations, new references. V3:
minor changes - final version as published in Phys. Rev. Let
Auxiliary matrix formalism for interaction representation transformations, optimal control and spin relaxation theories
Auxiliary matrix exponential method is used to derive simple and numerically
efficient general expressions for the following, historically rather cumbersome
and hard to compute, theoretical methods: (1) average Hamiltonian theory
following interaction representation transformations; (2)
Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3)
gradient ascent pulse engineering version of quantum optimal control theory. In
the context of spin dynamics, the auxiliary matrix exponential method is more
efficient than methods based on matrix factorizations and also exhibits more
favourable complexity scaling with the dimension of the Hamiltonian matrix
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