62,157 research outputs found
Optical modes in linear arrays of dielectric spherical particles: A numerical investigation
We have investigated bound modes in finite linear chains of dielectric
particles of various lengths, interparticle spacing and particle materials.
Through a unique application of the multisphere Mie scattering formalism, we
have developed numerical methods to calculate eigen-optical modes for various
arrays of particles. These numerical methods involve the use of the multisphere
scattering formalism as the entries in NxN matrices where N represents the
number of particles in the chain. Eigenmodes of these matrices correspond to
the eigen-optical modes of interest. We identified the eigenmodes with the
highest quality factor by the application of a modified version of the
Newton-Raphson algorithm. We found that convergence is strong using this
algorithm for linear chains of up to several hundreds of particles. By
comparing the dipolar approach with the more complex approach which utilizes a
combination of both dipolar and quadrupolar approaches, we demonstrated that
the dipolar approach has an accuracy of approximately 99%. We found that the
quality factor Q of the mode increases with the cubed value of the number of
particles in chain in agreement with the previously developed theory, the
effects of disordering of particle sizes and inter-particle distances will be
discussed.Comment: Submitted to Proceedings of SPI
Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap
A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic
trap with quadratic and quartic radial confinement is studied analytically with
the Thomas-Fermi approximation and numerically with the full time-independent
Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed
to exceed the radial harmonic frequency . In the regime
, the condensate contains a dense vortex array
(approximated as solid-body rotation for the analytical studies). At a critical
angular velocity , a central hole appears in the condensate.
Numerical studies confirm the predicted value of , even for
interaction parameters that are not in the Thomas-Fermi limit. The behavior is
also investigated at larger angular velocities, where the system is expected to
undergo a transition to a giant vortex (with pure irrotational flow).Comment: 14 pages, 5 figure
Measurements of the Influence of Acceleration and Temperature of Bodies on their Weight
A brief review of experimental research of the influence of acceleration and
temperatures of test mass upon gravitation force, executed between the 1990s
and the beginning of 2000 is provided.Results of weighing a rotor of a
mechanical gyroscope with a horizontal axis, an anisotropic crystal with the
big difference of the speed of longitudinal acoustic waves, measurements of
temperature dependence of weight of metal bars of non-magnetic materials, and
also measurement of restitution coefficients at quasi-elastic impact of a steel
ball about a massive plate are given. A negative temperature dependence of the
weight of a brass core was measured. All observably experimental effects, have
probably a general physical reason connected with the weight change dependent
upon acceleration of a body or at thermal movement of its microparticles.Comment: 7 pages, 6 figures. Presented at the 5-th Symposium on New Frontiers
and Future Concepts (STAIF-2008
Towards active microfluidics: Interface turbulence in thin liquid films with floating molecular machines
Thin liquid films with floating active protein machines are considered.
Cyclic mechanical motions within the machines, representing microscopic
swimmers, lead to molecular propulsion forces applied to the air-liquid
interface. We show that, when the rate of energy supply to the machines exceeds
a threshold, the flat interface becomes linearly unstable. As the result of
this instability, the regime of interface turbulence, characterized by
irregular traveling waves and propagating machine clusters, is established.
Numerical investigations of this nonlinear regime are performed. Conditions for
the experimental observation of the instability are discussed.Comment: 9 pages, 8 figures, RevTeX, submitted to Physical Review
Flexoelectric effect in finite samples
Static flexoelectric effect in a finite sample of a solid is addressed in
terms of phenomenological theory for the case of a thin plate subjected to
bending. It has been shown that despite an explicit asymmetry inherent to the
bulk constitutive electromechanical equations which take into account the
flexoelectric coupling, the electromechanical response for a finite sample is
"symmetric". "Symmetric" means that if a sensor and an actuator are made of a
flexoelectric element, performance of such devices can be characterized by the
same effective piezoelectric coefficient. This behavior is consistent with the
thermodynamic arguments offered earlier, being in conflict with the current
point of view on the matter in literature. This result was obtained using
standard mechanical boundary conditions valid for the case where the
polarization vanishes at the surface. It was shown that, for the case where
there is the polarization is nonzero at the surface, the aforementioned
symmetry of electromechanical response may be violated if standard mechanical
boundary conditions are used, leading to a conflict with the thermodynamic
arguments. It was argued that this conflict may be resolved when using modified
mechanical boundary conditions. It was also shown that the contribution of
surface piezoelectricity to the flexoelectric response of a finite sample is
expected to be comparable to that of the static bulk contribution (including
the material with high values of the dielectric constant) and to scale as the
bulk value of the dielectric constant (similar to the bulk contribution). This
finding implies that if the experimentally measured flexoelectric coefficient
scales as the dielectric constant of the material, this does not imply that the
measured flexoelectric response is controlled by the static bulk contribution
to the flexoelectric effect
Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
A key feature of ground states of gapped local 1D Hamiltonians is their
relatively low entanglement --- they are well approximated by matrix product
states (MPS) with bond dimension scaling polynomially in the length of the
chain, while general states require a bond dimension scaling exponentially. We
show that the bond dimension of these MPS approximations can be improved to a
constant, independent of the chain length, if we relax our notion of
approximation to be more local: for all length- segments of the chain, the
reduced density matrices of our approximations are -close to those of
the exact state. If the state is a ground state of a gapped local Hamiltonian,
the bond dimension of the approximation scales like ,
and at the expense of worse but still scaling of
the bond dimension, we give an alternate construction with the additional
features that it can be generated by a constant-depth quantum circuit with
nearest-neighbor gates, and that it applies generally for any state with
exponentially decaying correlations. For a completely general state, we give an
approximation with bond dimension , which is exponentially
worse, but still independent of . Then, we consider the prospect of
designing an algorithm to find a local approximation for ground states of
gapped local 1D Hamiltonians. When the Hamiltonian is translationally
invariant, we show that the ability to find -accurate local
approximations to the ground state in time implies the ability to
estimate the ground state energy to precision in time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction
for general states; Lemma 7 & Theorem 2 slightly improved; figures added;
lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional
references inserte
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