77,917 research outputs found
Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions
We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2AāA+,x, t>0, ||t=ā||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1<p<()+, q>0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1<p<1+4/N or if r=p+1 and 1<p<, then for aA>1 and sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 1<p3 or if r=p+1 and 1<p<, then for 0<aA<1 the near-boundary spike is stable. (iii) For N=1 if 3<p<5 and r=2, then there exist a0(0,1) and Āµ0>1 such that for a(a0,1) and Āµ=2q/(s+1)(pā1)(1,Āµ0) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as 0. Ā©2007 American Institute of Physic
Enhanced Ferromagnetic Stability in Cu Doped Passivated GaN Nanowires
Density functional calculations are performed to investigate the room
temperature ferromagnetism in GaN:Cu nanowires (NWs). Our results indicate that
two Cu dopants are most stable when they are near each other. Compared to bulk
GaN:Cu, we find that magnetization and ferromagnetism in Cu doped NWs is
strongly enhanced because the band width of the Cu td band is reduced due to
the 1D nature of the NW. The surface passivation is shown to be crucial to
sustain the ferromagnetism in GaN:Cu NWs. These findings are in good agreement
with experimental observations and indicate that ferromagnetism in this type of
systems can be tuned by controlling the size or shape of the host materials.Comment: Nano Lett., ASAP Article, 10.1021/nl080261
Existence and Stability of a Spike in the Central Component for a Consumer Chain Model
We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir
Effects of topological edge states on the thermoelectric properties of Bi nanoribbons
Using first-principles calculations combined with Boltzmann transport theory,
we investigate the effects of topological edge states on the thermoelectric
properties of Bi nanoribbons. It is found that there is a competition between
the edge and bulk contributions to the Seebeck coefficients. However, the
electronic transport of the system is dominated by the edge states because of
its much larger electrical conductivity. As a consequence, a room temperature
value exceeding 3.0 could be achieved for both p- and n-type systems when the
relaxation time ratio between the edge and the bulk states is tuned to be 1000.
Our theoretical study suggests that the utilization of topological edge states
might be a promising approach to cross the threshold of the industrial
application of thermoelectricity
Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation
The classical dynamics for a charged point particle with intrinsic spin is
governed by a relativistic Hamiltonian for the orbital motion and by the
Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is
natural to ask whether the classical Hamiltonian (with both the orbital and
spin parts) is consistent with that in the relativistic quantum theory for a
spin-1/2 charged particle, which is described by the Dirac equation. In the
low-energy limit, up to terms of the 7th order in ( and
is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation
of the Dirac Hamiltonian in the presence of homogeneous and static
electromagnetic fields and show that it is indeed in agreement with the
classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through
electromagnetic duality, this result can be generalized for a spin-1/2 dyon,
which has both electric and magnetic charges and thus possesses both intrinsic
electric and magnetic dipole moments. Furthermore, the relativistic quantum
theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and
gyroelectric ratios can be described by the Dirac-Pauli equation, which is the
Dirac equation with augmentation for the anomalous electric and anomalous
magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian
is shown, up to the 7th order again, to be also in accord with the classical
Hamiltonian.Comment: 18 page
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