11,489 research outputs found
From nothing to something: discrete integrable systems
Chinese ancient sage Laozi said that everything comes from `nothing'.
Einstein believes the principle of nature is simple. Quantum physics proves
that the world is discrete. And computer science takes continuous systems as
discrete ones. This report is devoted to deriving a number of discrete models,
including well-known integrable systems such as the KdV, KP, Toda, BKP, CKP,
and special Viallet equations, from `nothing' via simple principles. It is
conjectured that the discrete models generated from nothing may be integrable
because they are identities of simple algebra, model-independent nonlinear
superpositions of a trivial integrable system (Riccati equation), index
homogeneous decompositions of the simplest geometric theorem (the angle
bisector theorem), as well as the M\"obious transformation invariants.Comment: 11 pages, side 10 repor
A new approach to optimal control of conductance-based spiking neurons
This paper presents an algorithm for solving the minimum-energy optimal control problem of conductance-based spiking neurons. The basic procedure is (1) to construct a conductance-based spiking neuron oscillator as an affine nonlinear system, (2) to formulate the optimal control problem of the affine nonlinear system as a boundary value problem based on the Pontryagin’s maximum principle, and (3) to solve the boundary value problem using the homotopy perturbation method. The construction of the minimum-energy optimal control in the framework of the homotopy perturbation technique is novel and valid for a broad class of nonlinear conductance-based neuron models. The applicability of our method in the FitzHugh-Nagumo and Hindmarsh-Rose models is validated by simulations
Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity
Nonlinear localized excitations in one-dimensional diatomic lattices with
cubic and quartic nonlinearity are considered analytically by a
quasi-discreteness approach. The criteria for the occurence of asymmetric gap
solitons (with vibrating frequency lying in the gap of phonon bands) and
small-amplitude, asymmetric intrinsic localized modes (with the vibrating
frequency being above all the phonon bands) are obtained explicitly based on
the modulational instabilities of corresponding linear lattice plane waves. The
expressions of particle displacement for all these nonlinear localized
excitations are also given. The result is applied to standard two-body
potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The
comparison with previous numerical study of the anharmonic gap modes in
diatomic lattices for the standard two-body potentials is made and good
agreement is found.Comment: 24 pages in Revtex, 2 PS figure
Theory and laboratory astrophysics
Science opportunities in the 1990's are discussed. Topics covered include the large scale structure of the universe, galaxies, stars, star formation and the interstellar medium, high energy astrophysics, and the solar system. Laboratory astrophysics in the 1990's is briefly surveyed, covering such topics as molecular, atomic, optical, nuclear and optical physics. Funding recommendations are given for the National Science Foundation, NASA, and the Department of Energy. Recommendations for laboratory astrophysics research are given
Low-energy properties and magnetization plateaus in a 2-leg mixed spin ladder
Using the density matrix renormalization group technique we investigate the
low-energy properties and the magnetization plateau behavior in a 2-leg mixed
spin ladder consisting of a spin-1/2 chain coupled with a spin-1 chain. The
calculated results show that the system is in the same universality class as
the spin-3/2 chain when the interchain coupling is strongly ferromagnetic, but
the similarity between the two systems is less clear under other coupling
conditions. We have identified two types of magnetization plateau phases. The
calculation of the magnetization distribution on the spin-1/2 and the spin-1
chains on the ladder shows that one plateau phase is related to the partially
magnetized valence-bond-solid state, and the other plateau state contains
strongly coupled S=1 and s=1/2 spins on the rung.Comment: 6 pages with 8 eps figure
Gaussian Wavefunctional Approach in Thermofield Dynamics
The Gaussian wavefunctional approach is developed in thermofield dynamics. We
manufacture thermal vacuum wavefunctional, its creation as well as annihilation
operators,and accordingly thermo-particle excited states. For a
(D+1)-dimensional scalar field system with an arbitrary potential whose Fourier
representation exists in a sense of tempered distributions, we calculate the
finite temperature Gaussian effective potential (FTGEP), one- and
two-thermo-particle-state energies. The zero-temperature limit of each of them
is just the corresponding result in quantum field theory, and the FTGEP can
lead to the same one of each of some concrete models as calculated by the
imaginary time Green function.Comment: the revised version of hep-th/9807025, with one equation being added,
a few sentences rewritten, and some spelling mistakes corrected. 7 page,
Revtex, no figur
Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram
We report a systematic study of the transition from a band insulator (BI) to
a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with
an on-site Coulomb interaction U and an alternating periodic site potential V.
We employ both the zero-temperature density matrix renormalization group (DMRG)
method to determine the gap and critical behavior of the system and the
finite-temperature transfer matrix renormalization group method to evaluate the
thermodynamic properties. We find two critical points at U = and U =
that separate the BI and MI phases for a given V. A charge-neutral
spin-singlet exciton band develops in the BI phase (U<) and drops below
the band gap when U exceeds a special point Ue. The exciton gap closes at the
first critical point while the charge and spin gaps persist and coincide
between <U< where the system is dimerized. Both the charge and spin
gaps collapse at U = when the transition to the MI phase occurs. In the
MI phase (U>) the charge gap increases almost linearly with U while the
spin gap remains zero. These findings clarify earlier published results on the
same model, and offer insights into several important issues regarding an
appropriate scaling analysis of DMRG data and a full physical picture of the
delicate nature of the phase transitions driven by electron correlation. The
present work provides a comprehensive understanding for the critical behavior
and phase diagram for the transition from BI to MI in one-dimensional
correlated electron systems with a periodic alternating site potential.Comment: long version, 10 figure
Film Edge Nonlocal Spin Valves
Spintronics is a new paradigm for integrated digital electronics. Recently
established as a niche for nonvolatile magnetic random access memory (MRAM), it
offers new functionality while demonstrating low power and high speed
performance. However, to reach high density spintronic technology must make a
transition to the nanometer scale. Prototype devices are presently made using a
planar geometry and have an area determined by the lithographic feature size,
currently about 100 nm. Here we present a new nonplanar geometry in which one
lateral dimension is given by a film thickness, the order of 10 nm. With this
new approach, cell sizes can shrink by an order of magnitude. The geometry is
demonstrated with a nonlocal spin valve, where we study devices with an
injector/detector separation much less than the spin diffusion length.Comment: 10 pages, 3 figure
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