3,420 research outputs found
Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
In a certain class of differential-difference equations for dissipative
systems, we show that hyperbolic tangent model is the only the nonlinear system
of equations which can admit some particular solutions of the Toda lattice. We
give one parameter family of exact solutions, which include as special cases
the Toda lattice solutions as well as the Whitham's solutions in the Newell's
model. Our solutions can be used to describe temporal-spatial density patterns
observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur
Supersonic crack propagation in a class of lattice models of Mode III brittle fracture
We study a lattice model for mode III crack propagation in brittle materials
in a stripe geometry at constant applied stretching. Stiffening of the material
at large deformation produces supersonic crack propagation. For large
stretching the propagation is guided by well developed soliton waves. For low
stretching, the crack-tip velocity has a universal dependence on stretching
that can be obtained using a simple geometrical argument.Comment: 4 pages, 3 figure
Lieb-Robinson Bounds for the Toda Lattice
We establish locality estimates, known as Lieb-Robinson bounds, for the Toda
lattice. In contrast to harmonic models, the Lieb-Robinson velocity for these
systems do depend on the initial condition. Our results also apply to the
entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable
assumptions, our methods also yield a finite velocity for certain perturbations
of these systems
Towards an Intraoral-Based Silent Speech Restoration System for Post-laryngectomy Voice Replacement
© Springer International Publishing AG 2017, Silent Speech Interfaces (SSIs) are alternative assistive speech technologies that are capable of restoring speech communication for those individuals who have lost their voice due to laryngectomy or diseases affecting the vocal cords. However, many of these SSIs are still deemed as impractical due to a high degree of intrusiveness and discomfort, hence limiting their transition to outside of the laboratory environment. We aim to address the hardware challenges faced in developing a practical SSI for post-laryngectomy speech rehabilitation. A new Permanent Magnet Articulography (PMA) system is presented which fits within the palatal cavity of the user’s mouth, giving unobtrusive appearance and high portability. The prototype is comprised of a miniaturized circuit constructed using commercial off-the-shelf (COTS) components and is implemented in the form of a dental retainer, which is mounted under roof of the user’s mouth and firmly clasps onto the upper teeth. Preliminary evaluation via speech recognition experiments demonstrates that the intraoral prototype achieves reasonable word recognition accuracy and is comparable to the external PMA version. Moreover, the intraoral design is expected to improve on its stability and robustness, with a much improved appearance since it can be completely hidden inside the user’s mouth
A class of integrable lattices and KP hierarchy
We introduce a class of integrable -field first-order lattices together
with corresponding Lax equations. These lattices may be represented as
consistency condition for auxiliary linear systems defined on sequences of
formal dressing operators. This construction provides simple way to build
lattice Miura transformations between one-field lattice and -field () ones. We show that the lattices pertained to above class is in some sense
compatible with KP flows and define the chains of constrained KP Lax operators.Comment: LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge
Processing Succinct Matrices and Vectors
We study the complexity of algorithmic problems for matrices that are
represented by multi-terminal decision diagrams (MTDD). These are a variant of
ordered decision diagrams, where the terminal nodes are labeled with arbitrary
elements of a semiring (instead of 0 and 1). A simple example shows that the
product of two MTDD-represented matrices cannot be represented by an MTDD of
polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by
allowing componentwise symbolic addition of variables (of the same dimension)
in rules. It is shown that accessing an entry, equality checking, matrix
multiplication, and other basic matrix operations can be solved in polynomial
time for MTDD_+-represented matrices. On the other hand, testing whether the
determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the
same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing
a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of
CSR 201
Taylor dispersion with absorbing boundaries: A Stochastic Approach
We describe how to solve the problem of Taylor dispersion in the presence of
absorbing boundaries using an exact stochastic formulation. In addition to
providing a clear stochastic picture of Taylor dispersion, our method leads to
closed-form expressions for all the moments of the convective displacement of
the dispersing particles in terms of the transverse diffusion eigenmodes. We
also find that the cumulants grow asymptotically linearly with time, ensuring a
Gaussian distribution in the long-time limit. As a demonstration of the
technique, the first two longitudinal cumulants (yielding respectively the
effective velocity and the Taylor diffusion constant) as well as the skewness
(a measure of the deviation from normality) are calculated for fluid flow in
the parallel plate geometry. We find that the effective velocity and the
skewness (which is negative in this case) are enhanced while Taylor dispersion
is suppressed due to absorption at the boundary.Comment: 4 pages, 1 figur
Integrable dynamics of Toda-type on the square and triangular lattices
In a recent paper we constructed an integrable generalization of the Toda law
on the square lattice. In this paper we construct other examples of integrable
dynamics of Toda-type on the square lattice, as well as on the triangular
lattice, as nonlinear symmetries of the discrete Laplace equations on the
square and triangular lattices. We also construct the - function
formulations and the Darboux-B\"acklund transformations of these novel
dynamics.Comment: 22 pages, 4 figure
Point Symmetries of Generalized Toda Field Theories
A class of two-dimensional field theories with exponential interactions is
introduced. The interaction depends on two ``coupling'' matrices and is
sufficiently general to include all Toda field theories existing in the
literature. Lie point symmetries of these theories are found for an infinite,
semi-infinite and finite number of fields. Special attention is accorded to
conformal invariance and its breaking.Comment: 25 pages, no figures, Latex fil
Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain
We study an asymptotic behavior of a special correlator known as the
Emptiness Formation Probability (EFP) for the one-dimensional anisotropic XY
spin-1/2 chain in a transverse magnetic field. This correlator is essentially
the probability of formation of a ferromagnetic string of length in the
antiferromagnetic ground state of the chain and plays an important role in the
theory of integrable models. For the XY Spin Chain, the correlator can be
expressed as the determinant of a Toeplitz matrix and its asymptotical
behaviors for throughout the phase diagram are obtained using
known theorems and conjectures on Toeplitz determinants. We find that the decay
is exponential everywhere in the phase diagram of the XY model except on the
critical lines, i.e. where the spectrum is gapless. In these cases, a power-law
prefactor with a universal exponent arises in addition to an exponential or
Gaussian decay. The latter Gaussian behavior holds on the critical line
corresponding to the isotropic XY model, while at the critical value of the
magnetic field the EFP decays exponentially. At small anisotropy one has a
crossover from the Gaussian to the exponential behavior. We study this
crossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due
to arxiv space limitations. If You would like to see the pdf with good
quality figures, please contact Fabio Franchini at
"[email protected]
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