103 research outputs found
Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors
An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk
n-GaAs with circular contacts is presented. A moving pulse far from contacts is
approximated by a moving free boundary separating regions where the electric
potential solves a Laplace equation with subsidiary boundary conditions. The
dynamical condition for the motion of the free boundary is a Hamilton-Jacobi
equation. We obtain the exact solution of the free boundary problem (FBP) in
simple one-dimensional and axisymmetric geometries. The solution of the FBP is
obtained numerically in the general case and compared with the numerical
solution of the full system of equations. The agreement is excellent so that
the FBP can be adopted as the basis for an asymptotic study of the
multi-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.
Theory of charge fluctuations and domain relocation times in semiconductor superlattices
Shot noise affects differently the nonlinear electron transport in
semiconductor superlattices depending on the strength of the coupling among the
superlattice quantum wells. Strongly coupled superlattices can be described by
a miniband Boltzmann-Langevin equation from which a stochastic drift-diffusion
equation is derived by means of a consistent Chapman-Enskog method. Similarly,
shot noise in weakly coupled, highly doped semiconductor superlattices is
described by a stochastic discrete drift-diffusion model. The current-voltage
characteristics of the corresponding deterministic model consist of a number of
stable branches corresponding to electric field profiles displaying two domains
separated by a domain wall. If the initial state corresponds to a voltage on
the middle of a stable branch and is suddenly switched to a final voltage
corresponding to the next branch, the domains relocate after a certain delay
time, called relocation time. The possible scalings of this mean relocation
time are discussed using bifurcation theory and the classical results for
escape of a Brownian particle from a potential well.Comment: 14 pages, 2 figure
Axisymmetric pulse recycling and motion in bulk semiconductors
The Kroemer model for the Gunn effect in a circular geometry (Corbino disks)
has been numerically solved. The results have been interpreted by means of
asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric
pulses of the electric field are periodically shed by an inner circular
cathode. These pulses decay as they move towards the outer anode, which they
may not reach. As a pulse advances, the external current increases continuously
until a new pulse is generated. Then the current abruptly decreases, in
agreement with existing experimental results. Depending on the bias, more
complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure
Asymptotics of the trap-dominated Gunn effect in p-type Ge
We present an asymptotic analysis of the Gunn effect in a drift-diffusion
model---including electric-field-dependent generation-recombination
processes---for long samples of strongly compensated p-type Ge at low
temperature and under dc voltage bias. During each Gunn oscillation, there are
different stages corresponding to the generation, motion and annihilation of
solitary waves. Each stage may be described by one evolution equation for only
one degree of freedom (the current density), except for the generation of each
new wave. The wave generation is a faster process that may be described by
solving a semiinfinite canonical problem. As a result of our study we have
found that (depending on the boundary condition) one or several solitary waves
may be shed during each period of the oscillation. Examples of numerical
simulations validating our analysis are included.Comment: Revtex, 25 pag., 5 fig., to appear Physica
Protein unfolding and refolding as transitions through virtual states
Single-molecule atomic force spectroscopy probes elastic properties of titin, ubiquitin and other relevant proteins. We explain bioprotein folding dynamics under both length- and force-clamp by modeling polyprotein modules as particles in a bistable potential, weakly connected by harmonic spring linkers. Multistability of equilibrium extensions provides the characteristic sawtooth force-extension curve. We show that abrupt or stepwise unfolding and refolding under force-clamp conditions involve transitions through virtual states (which are quasi-stationary domain configurations) modified by thermal noise. These predictions agree with experimental observations
Aging in the Linear Harmonic Oscillator
The low temperature Monte Carlo dynamics of an ensemble of linear harmonic
oscillators shows some entropic barriers related to the difficulty of finding
the directions in configurational space which decrease the energy. This
mechanism is enough to observe some typical non-equilibrium features of glassy
systems like activated-type behavior and aging in the correlation function and
in the response function. Due to the absence of interactions the model only
displays a one-step relaxation process.Comment: 6 pages revtex including 3 figures in postscrip
Kinetics of helium bubble formation in nuclear materials
The formation and growth of helium bubbles due to self-irradiation in
plutonium has been modelled by a discrete kinetic equations for the number
densities of bubbles having atoms. Analysis of these equations shows that
the bubble size distribution function can be approximated by a composite of:
(i) the solution of partial differential equations describing the continuum
limit of the theory but corrected to take into account the effects of
discreteness, and (ii) a local expansion about the advancing leading edge of
the distribution function in size space. Both approximations contribute to the
memory term in a close integrodifferential equation for the monomer
concentration of single helium atoms.
The present boundary layer theory for discrete equations is compared to the
numerical solution of the full kinetic model and to previous approximation of
Schaldach and Wolfer involving a truncated system of moment equations.Comment: 24 pages, 6 figures, to appear in Physica
Effects of disorder on the wave front depinning transition in spatially discrete systems
Pinning and depinning of wave fronts are ubiquitous features of spatially
discrete systems describing a host of phenomena in physics, biology, etc. A
large class of discrete systems is described by overdamped chains of nonlinear
oscillators with nearest-neighbor coupling and subject to random external
forces. The presence of weak randomness shrinks the pinning interval and it
changes the critical exponent of the wave front depinning transition from 1/2
to 3/2. This effect is derived by means of a recent asymptotic theory of the
depinning transition, extended to discrete drift-diffusion models of transport
in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.
Synchronization in populations of globally coupled oscillators with inertial effects
A model for synchronization of globally coupled phase oscillators including
``inertial'' effects is analyzed. In such a model, both oscillator frequencies
and phases evolve in time. Stationary solutions include incoherent
(unsynchronized) and synchronized states of the oscillator population. Assuming
a Lorentzian distribution of oscillator natural frequencies, , both
larger inertia or larger frequency spread stabilize the incoherent solution,
thereby making harder to synchronize the population. In the limiting case
, the critical coupling becomes independent of
inertia. A richer phenomenology is found for bimodal distributions. For
instance, inertial effects may destabilize incoherence, giving rise to
bifurcating synchronized standing wave states. Inertia tends to harden the
bifurcation from incoherence to synchronized states: at zero inertia, this
bifurcation is supercritical (soft), but it tends to become subcritical (hard)
as inertia increases. Nonlinear stability is investigated in the limit of high
natural frequencies.Comment: Revtex, 36 pages, submit to Phys. Rev.
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