18,338 research outputs found
Bessel Functions in Mass Action. Modeling of Memories and Remembrances
Data from experimental observations of a class of neurological processes
(Freeman K-sets) present functional distribution reproducing Bessel function
behavior. We model such processes with couples of damped/amplified oscillators
which provide time dependent representation of Bessel equation. The root loci
of poles and zeros conform to solutions of K-sets. Some light is shed on the
problem of filling the gap between the cellular level dynamics and the brain
functional activity. Breakdown of time-reversal symmetry is related with the
cortex thermodynamic features. This provides a possible mechanism to deduce
lifetime of recorded memory.Comment: 16 pages, 9 figures, Physics Letters A, 2015 in pres
Quantum state transfer for multi-input linear quantum systems
Effective state transfer is one of the most important problems in quantum
information processing. Typically, a quantum information device is composed of
many subsystems with multi-input ports. In this paper, we develop a general
theory describing the condition for perfect state transfer from the multi-input
ports to the internal system components, for general passive linear quantum
systems. The key notion used is the zero of the transfer function matrix.
Application to entanglement generation and distribution in a quantum network is
also discussed.Comment: 6 pages, 3 figures. A preliminary condensed version of this work will
appear in Proceedings of the 55th IEEE Conference on Decision and Contro
Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation
Pade approximants are used to find approximate vortex solutions of any
winding number in the context of Gross-Pitaevskii equation for a uniform
condensate and condensates with axisymmetric trapping potentials. Rational
function and generalised rational function approximations of axisymmetric
solitary waves of the Gross-Pitaevskii equation are obtained in two and three
dimensions. These approximations are used to establish a new mechanism of
vortex nucleation as a result of solitary wave interactions.Comment: In press by Journal of Physics: Mathematics and Genera
Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain
Quantum dynamics of magnetic order in a chiral multiferroic chain is studied.
We consider two different scenarios: Ultrashort terahertz (THz) excitations or
a sudden electric field quench. Performing analytical and numerical exact
diagonalization calculations we trace the pulse induced spin dynamics and
extract quantities that are relevant to quantum information processing. In
particular, we analyze the dynamics of the system chirality, the von Neumann
entropy, the pairwise and the many body entanglement. If the characteristic
frequencies of the generated states are non-commensurate then a partial loss of
pair concurrence occurs. Increasing the system size this effect becomes even
more pronounced. Many particle entanglement and chirality are robust and
persist in the incommensurate phase. To analyze the dynamical quantum
transitions for the quenched and pulsed dynamics we combined the Weierstrass
factorization technique for entire functions and Lanczos exact diagonalization
method. For a small system we obtained analytical results including the rate
function of Loschmidt echo. Exact numerical calculations for a system up to 40
spins confirm phase transition. Quench- induced dynamical transitions have been
extensively studied recently. Here we show that related dynamical transitions
can be achieved and controlled by appropriate electric field pulses.Comment: 13 pages, 10 figures, submitted in PR
Active Vibration Control of Structures using an Impedance Matching Control Technique
Active vibration control of structures has gained a lot of interest in recent years. This paper presents an active vibration control methodology of a structure using piezoelectric actuators. The proposed methodology is useful in practical applications where the system to be controlled is difficult to model due to the presence of complex boundary conditions. The impedance matching control technique uses a power flow approach wherein the controller is designed such that the power flow into the structure is minimized. The system transfer function is obtained from the experimental collocated actuator/sensor pair data using Eigen Realisation Algorithm (ERA). The controller is designed for the system transfer function according to impedance matching theory. The above approach is targeted towards the vibration control of wind tunnel stings, which suffer from flow-induced vibration. A wind tunnel sting model is designed and fabricated for this study. The real time implementation of the impedance matching controller has been carried out using dSPACE® Digital Signal Processor (DSP) card. The results are encouraging and demonstrate the feasibility of applying this technique in the wind tunne
Generalizations of the sampling theorem: Seven decades after Nyquist
The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed
Interactions of vortices with rarefaction solitary waves in a Bose-Einstein condensate and their role in the decay of superfluid turbulence
There are several ways to create the vorticity-free solitary waves --
rarefaction pulses -- in condensates: by the process of strongly nonequilibrium
condensate formation in a weakly interacting Bose gas, by creating local
depletion of the condensate density by a laser beam, and by moving a small
object with supercritical velocities. Perturbations created by such waves
colliding with vortices are studied in the context of the Gross-Pitaevskii
model. We find that the effect of the interactions consists of two competing
mechanisms: the creation of vortex line as rarefaction waves acquire
circulation in a vicinity of a vortex core and the loss of the vortex line to
sound due to Kelvin waves that are generated on vortex lines by rarefaction
pulses. When a vortex ring collides with a rarefaction wave, the ring either
stabilises to a smaller ring after emitting sound through Kelvin wave radiation
or the entire energy of the vortex ring is lost to sound if the radius of the
ring is of the order of the healing length. We show that during the time
evolution of a tangle of vortices, the interactions with rarefaction pulses
provide an important dissipation mechanism enhancing the decay of superfluid
turbulence.Comment: Revised paper accepted by Phys. Rev.
- …