364 research outputs found
Marangoni instability in oblate droplets suspended on a circular frame
We study theoretically internal flows in a small oblate droplet suspended on
the circular frame. Marangoni convection arises due to a vertical temperature
gradient across the drop and is driven by the surface tension variations at the
free drop interface. Using the analytical basis for the solutions of Stokes
equation in coordinates of oblate spheroid we have derived the linearly
independent stationary solutions for Marangoni convection in terms of Stokes
stream functions. The numerical simulations of the thermocapillary motion in
the drops are used to study the onset of the stationary regime. Both analytical
and numerical calculations predict the axially-symmetric circulatory convection
motion in the drop, the dynamics of which is determined by the magnitude of the
temperature gradient across the drop. The analytical solutions for the critical
temperature distribution and velocity fields are obtained for the large
temperature gradients across the oblate drop. These solutions reveal the
lateral separation of the critical and stationary motions within the drops. The
critical vortices are localized near the central part of a drop, while the
intensive stationary flow is located closer to its butt end. A crossover to the
limit of the plane film is studied within the formalism of the stream functions
by reducing the droplet ellipticity ratio to zero value. The initial stationary
regime for the strongly oblate drops becomes unstable relative to the
many-vortex perturbations in analogy with the plane fluid films with free
boundaries
Circulating Marangoni flows within droplets in smectic films
We present theoretical study and numerical simulation of Marangoni convection
within ellipsoidal isotropic droplets embedded in free standing smectic films
(FSSF). The thermocapillary flows are analyzed for both isotropic droplets
spontaneously formed in FSSF overheated above the bulk smectic-isotropic
transition, and oil lenses deposited on the surface of the smectic film. The
realistic model, for which the upper drop interface is free from the smectic
layers, while at the lower drop surface the smectic layering still persists is
considered in detail. For isotropic droplets and oil lenses this leads
effectively to a sticking of fluid motion at the border with a smectic shell.
The above mentioned asymmetric configuration is realized experimentally when
the temperature of the upper side of the film is higher than at the lower one.
The full set of stationary solutions for Stokes stream functions describing the
Marangoni convection flows within the ellipsoidal drops were derived
analytically. The temperature distribution in the ellipsoidal drop and the
surrounding air was determined in the frames of the perturbation theory. As a
result the analytical solutions for the stationary thermocapillary convection
were derived for different droplet ellipticity ratios and the heat conductivity
of the liquid crystal and air. In parallel, the numerical hydrodynamic
calculations of the thermocapillary motion in the drops were performed. Both
the analytical and numerical simulations predict the axially-symmetric
circulatory convection motion determined by the Marangoni effect at the droplet
free surface. Due to a curvature of the drop interface a temperature gradient
along its free surface always persists. Thus, the thermocapillary convection
within the ellipsoidal droplets in overheated FSSF is possible for the
arbitrarily small Marangoni numbers
Fabrication of submicron structures by three-dimensional laser lithography
As a demonstration of unique capabilities of three dimensional laser lithography, an example complex shape
microobject and photonic crystals with “woodpile” structure for the infrared spectral range are fabricated by
this technique. Photonic dispersion relations for the woodpile structure are calculated for different values of
the permittivity contrast and the filling factor.This study was partially supported by the
Government of the Russian Federation (project no.
074U01) and the Russian Foundation for Basic
Research (project no. 130200186)
Dual-channel spontaneous emission of quantum dots in magnetic metamaterials
Metamaterials, artificial electromagnetic media realized by subwavelength nano-structuring, have become a paradigm for engineering electromagnetic space, allowing for independent control of both electric and magnetic responses of the material. Whereas mo
Quantification of thermal ring flexibilities of aromatic and heteroaromatic compounds
The consequences of thermal fluctuations occurring at room temperatures on the aromatic character of a broad group of compounds were analyzed in three distinct ways. First of all, the ring deformations were modeled along normal coordinates coming from quantum thermo-chemistry computations. The amplitudes of vibrations were estimated according to absorbed energies at room temperature. Alternatively, in-plane and out-of-plane ring deformations were modeled via scanning procedure with partial relaxation of the molecular geometry. The influence of ring deformations on π–electron delocalization was expressed in terms of HOMA values. Besides, the ring deformability was defined as the averaged change of bond angles or dihedral angles constituting the ring that was associated with 1.5 kcal mol-1 increase of the system energy. The molecules structures adopted during vibrations at room temperature can lead to significant heterogeneity of structural index of aromaticity. The broad span of HOMA values was obtained for analyzed five- or six-membered aromatic and heteroaromatic rings. However, the averaged values obtained for such fluctuations almost perfectly match HOMA values of molecule in the ground state. It has been demonstrated that the ring deformability imposed by bond angle changes is much smaller than for dihedral angles with the same rise of system energy. Interestingly in the case of out-of-plane vibrations modeled by scanning procedure there is observed linear correlation between ring deformability and HOMA values. Proposed method for inclusion of thermal vibrations in the framework of π–electron delocalization provides natural shift of the way of thinking about aromaticity from a static quantity to a dynamic and heterogeneous one due to inclusion of a more realistic object of analysis – thermally deformed structures. From this perspective the thermal fluctuations are supposed to be non-negligible contributions to aromaticity phenomenon
The Dirac Equation Is Separable On The Dyon Black Hole Metric
Using the tetrad formalism, we carry out the separation of variables for the
massive complex Dirac equation in the gravitational and electromagnetic field
of a four-parameter (mass, angular momentum, electric and magnetic charges)
black hole.Comment: 13 page
Two-photon Lithography for 3D Magnetic Nanostructure Fabrication
Ferromagnetic materials have been utilised as recording media within data
storage devices for many decades. Confinement of the material to a two
dimensional plane is a significant bottleneck in achieving ultra-high recording
densities and this has led to the proposition of three dimensional (3D)
racetrack memories that utilise domain wall propagation along nanowires.
However, the fabrication of 3D magnetic nanostructures of complex geometry is
highly challenging and not easily achievable with standard lithography
techniques. Here, by using a combination of two-photon lithography and
electrochemical deposition, we show a new approach to construct 3D magnetic
nanostructures of complex geometry. The magnetic properties are found to be
intimately related to the 3D geometry of the structure and magnetic imaging
experiments provide evidence of domain wall pinning at a 3D nanostructured
junction
Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations
One may ask whether the relations between energy and frequency and between
momentum and wave vector, introduced for matter waves by de Broglie, are
rigorously valid in the presence of gravity. In this paper, we show this to be
true for Dirac equations in a background of gravitational and electromagnetic
fields. We first transform any Dirac equation into an equivalent canonical
form, sometimes used in particular cases to solve Dirac equations in a curved
spacetime. This canonical form is needed to apply the Whitham Lagrangian
method. The latter method, unlike the WKB method, places no restriction on the
magnitude of Planck's constant to obtain wave packets, and furthermore
preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac
fields in a curved spacetime, that the probability current has a Gordon
decomposition into a convection current and a spin current, and that the spin
current vanishes in the Whitham approximation, which explains the negligible
effect of spin on wave packet solutions, independent of the size of Planck's
constant. We further discuss the classical-quantum correspondence in a curved
spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham
equations. We show that the generalized de Broglie relations in a curved
spacetime are a direct consequence of Whitham's Lagrangian method, and not just
a physical hypothesis as introduced by Einstein and de Broglie, and by many
quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on
canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac
equations. Added section on Gordon decomposition of the probability current.
Encapsulated main results in the statement of Theorem
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