Differential expansion for link polynomials

The differential expansion is one of the key structures reflecting group theory properties of colored knot polynomials, which also becomes an important tool for evaluation of non-trivial Racah matrices. This makes highly desirable its extension from knots to links, which, however, requires knowledge of the $6j$-symbols, at least, for the simplest triples of non-coincident representations. Based on the recent achievements in this direction, we conjecture a shape of the differential expansion for symmetrically-colored links and provide a set of examples. Within this study, we use a special framing that is an unusual extension of the topological framing from knots to links. In the particular cases of Whitehead and Borromean rings links, the differential expansions are different from the previously discovered.Comment: 11 page

Non-axisymmetric instability of shear-banded Taylor-Couette flow

Recent experiments show that shear-banded flows of semi-dilute worm-like micelles in Taylor-Couette geometry exhibit a flow instability in the form of Taylor-like vortices. Here we perform the non-axisymmetric linear stability analysis of the diffusive Johnson-Segalman model of shear banding and show that the nature of this instability depends on the applied shear rate. For the experimentally relevant parameters, we find that at the beginning of the stress plateau the instability is driven by the interface between the bands, while most of the stress plateau is occupied by the bulk instability of the high-shear-rate band. Our work significantly alters the recently proposed stability diagram of shear-banded flows based on axisymmetric analysis.Comment: 6 pages, 5 figures, main text and supplementary material; accepted to Phys. Rev. Let

Internal and External Resonances of Dielectric Disks

Circular microresonators (microdisks) are micron sized dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analysed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal and external resonances can be found in the same region of the complex wavenumber plane. It is also shown that for both polarizations, the internal as well as external resonances can be classified by well defined azimuthal and radial modal indices.Comment: 5 pages, 8 figures, pdflate

Symmetric achromatic low-beta collider interaction region design concept

We present a new symmetry-based concept for an achromatic low-beta collider interaction region design. A specially-designed symmetric Chromaticity Compensation Block (CCB) induces an angle spread in the passing beam such that it cancels the chromatic kick of the final focusing quadrupoles. Two such CCBs placed symmetrically around an interaction point allow simultaneous compensation of the 1st-order chromaticities and chromatic beam smear at the IP without inducing significant 2nd-order aberrations to the particle trajectory. We first develop an analytic description of this approach and explicitly formulate 2nd-order aberration compensation conditions at the interaction point. The concept is next applied to develop an interaction region design for the ion collider ring of an electron-ion collider. We numerically evaluate performance of the design in terms of momentum acceptance and dynamic aperture. The advantages of the new concept are illustrated by comparing it to the conventional distributed-sextupole chromaticity compensation scheme.Comment: 12 pages, 17 figures, to be submitted to Phys. Rev. ST Accel. Beam

A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

How the Proximal Pocket May Influence the Enantiospecificities of Chloroperoxidase-Catalyzed Epoxidations of Olefins

Chloroperoxidase-catalyzed enantiospecific epoxidations of olefins are of significant biotechnological interest. Typical enantiomeric excesses are in the range of 66%–97% and translate into free energy differences on the order of 1 kcal/mol. These differences are generally attributed to the effect of the distal pocket. In this paper, we show that the influence of the proximal pocket on the electron transfer mechanism in the rate-limiting event may be just as significant for a quantitatively accurate account of the experimentally-measured enantiospecificities

Thermal diffusion by Brownian motion induced fluid stress

The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles sub jected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in the experiments of Duhr, et al[1]. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimental value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal fluctuations-fluid momentum flux coupling induces a gradient in the stress which leads to thermal migration in both systems.Comment: 6 pages, 5 figue