18,753 research outputs found
Structure of Stochastic Dynamics near Fixed Points
We analyze the structure of stochastic dynamics near either a stable or
unstable fixed point, where force can be approximated by linearization. We find
that a cost function that determines a Boltzmann-like stationary distribution
can always be defined near it. Such a stationary distribution does not need to
satisfy the usual detailed balance condition, but might have instead a
divergence-free probability current. In the linear case the force can be split
into two parts, one of which gives detailed balance with the diffusive motion,
while the other induces cyclic motion on surfaces of constant cost function.
Using the Jordan transformation for the force matrix, we find an explicit
construction of the cost function. We discuss singularities of the
transformation and their consequences for the stationary distribution. This
Boltzmann-like distribution may be not unique, and nonlinear effects and
boundary conditions may change the distribution and induce additional currents
even in the neighborhood of a fixed point.Comment: 7 page
Globular Structures of a Helix-Coil Copolymer: Self-Consistent Treatment
A self-consistent field theory was developed in the grand-canonical ensemble
formulation to study transitions in a helix-coil multiblock globule. Helical
and coil parts are treated as stiff rods and self-avoiding walks of variable
lengths correspondingly. The resulting field-theory takes, in addition to the
conventional Zimm-Bragg (B.H. Zimm, I.K. Bragg, J. Chem. Phys. 31, 526 (1959))
parameters, also three-dimensional interaction terms into account. The
appropriate differential equations which determine the self-consistent fields
were solved numerically with finite element method. Three different phase
states are found: open chain, amorphous globule and nematic liquid-crystalline
(LC) globule. The LC-globule formation is driven by the interplay between the
hydrophobic helical segments attraction and the anisotropic globule surface
energy of an entropic nature. The full phase diagram of the helix-coil
copolymer was calculated and thoroughly discussed. The suggested theory shows a
clear interplay between secondary and tertiary structures in globular
homopolypeptides.Comment: 26 pages, 30 figures, corrected some typo
Field enhancement in subnanometer metallic gaps
Motivated by recent experiments [Ward et al., Nature Nanotech. 5, 732
(2010)], we present here a theoretical analysis of the optical response of
sharp gold electrodes separated by a subnanometer gap. In particular, we have
used classical finite difference time domain simulations to investigate the
electric field distribution in these nanojunctions upon illumination. Our
results show a strong confinement of the field within the gap region, resulting
in a large enhancement compared to the incident field. Enhancement factors
exceeding 1000 are found for interelectrode distances on the order of a few
angstroms, which are fully compatible with the experimental findings. Such huge
enhancements originate from the coupling of the incident light to the
evanescent field of hybrid plasmons involving charge density oscillations in
both electrodes.Comment: 4 pages, 3 figures, to appear in Physical Review
Construct, Merge, Solve and Adapt: Application to the repetition-free longest common subsequence problem
In this paper we present the application of a recently proposed, general, algorithm for combinatorial optimization to the repetition-free longest common subsequence problem. The applied algorithm, which is labelled Construct, Merge, Solve & Adapt, generates sub-instances based on merging the solution components found in randomly constructed solutions. These sub-instances are subsequently solved by means of an exact solver. Moreover, the considered sub-instances are dynamically changing due to adding new solution components at each iteration, and removing existing solution components on the basis of indicators about their usefulness. The results of applying this algorithm to the repetition-free longest common subsequence problem show that the algorithm generally outperforms competing approaches from the literature. Moreover, they show that the algorithm is competitive with CPLEX for small and medium size problem instances, whereas it outperforms CPLEX for larger problem instances.Peer ReviewedPostprint (author's final draft
High-performance functional renormalization group calculations for interacting fermions
We derive a novel computational scheme for functional Renormalization Group
(fRG) calculations for interacting fermions on 2D lattices. The scheme is based
on the exchange parametrization fRG for the two-fermion interaction, with
additional insertions of truncated partitions of unity. These insertions
decouple the fermionic propagators from the exchange propagators and lead to a
separation of the underlying equations. We demonstrate that this separation is
numerically advantageous and may pave the way for refined, large-scale
computational investigations even in the case of complex multiband systems.
Furthermore, on the basis of speedup data gained from our implementation, it is
shown that this new variant facilitates efficient calculations on a large
number of multi-core CPUs. We apply the scheme to the , Hubbard model on
a square lattice to analyze the convergence of the results with the bond length
of the truncation of the partition of unity. In most parameter areas, a fast
convergence can be observed. Finally, we compare to previous results in order
to relate our approach to other fRG studies.Comment: 26 pages, 9 figure
Phase behavior of the Confined Lebwohl-Lasher Model
The phase behavior of confined nematogens is studied using the Lebwohl-Lasher
model. For three dimensional systems the model is known to exhibit a
discontinuous nematic-isotropic phase transition, whereas the corresponding two
dimensional systems apparently show a continuous
Berezinskii-Kosterlitz-Thouless like transition. In this paper we study the
phase transitions of the Lebwohl-Lasher model when confined between planar
slits of different widths in order to establish the behavior of intermediate
situations between the pure planar model and the three-dimensional system, and
compare with previous estimates for the critical thickness, i.e. the slit width
at which the transition switches from continuous to discontinuous.Comment: Submitted to Physical Review
Unified algebraic treatment of resonance
Energy resonance in scattering is usually investigated either directly in the
complex energy plane (E-plane) or indirectly in the complex angular momentum
plane (L-plane). Another formulation complementing these two approaches was
introduced recently. It is an indirect algebraic method that studies resonances
in a complex charge plane (Z-plane). This latter approach will be generalized
to provide a unified algebraic treatment of resonances in the complex E-, L-,
and Z-planes. The complex scaling (rotation) method will be used in the
development of this approach. The resolvent operators (Green's functions) are
formally defined in these three spaces. Bound states spectrum and resonance
energies in the E-plane are mapped onto a discrete set of poles of the
respective resolvent operator on the real line of the L- and Z-planes. These
poles move along trajectories as the energy is varied. A finite square
integrable basis is used in the numerical implementation of this approach.
Stability of poles and trajectories against variation in all computational
parameters is demonstrated. Resonance energies for a given potential are
calculated and compared with those obtained by other studies.Comment: 15 pages, 1 Table, 7 Figures (6 are snapshots of videos
Fundamental Behavior of Electric Field Enhancements in the Gaps Between Closely Spaced Nanostructures
We demonstrate that the electric field enhancement that occurs in a gap
between two closely spaced nanostructures, such as metallic nanoparticles, is
the result of a transverse electromagnetic waveguide mode. We derive an
explicit semianalytic equation for the enhancement as a function of gap size,
which we show has a universal qualitative behavior in that it applies
irrespective of the material or geometry of the nanostructures and even in the
presence of surface plasmons. Examples of perfect electrically conducting and
Ag thin-wire antennas and a dimer of Ag spheres are presented and discussed.Comment: 9 pages and 4 figure
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