Kinetic considerations of the strength of oriented solids

Kinetics of mechanical strength of oriented and stressed solids based on statistical absolute reaction rate theor

H. C. Ting Letter

A letter from a former student of Theora England, H. C. Ting, given to her on her retirement.https://nwcommons.nwciowa.edu/theorareflections/1021/thumbnail.jp

Quantum interference in dirty d-wave superconductors

The local differential tunneling conductance on a Zn impurity in a disordered d-wave superconductors is studied. Quantum interference between many impurities leads to definitive quasiparticle spectra. We suggest that an elaborate analysis on impurity-induced spectra with quantum interference effect included may be able to pin down the sign and strength of the scattering potential of a Zn impurity in low density limit. Numerical simulations calculated with appropriately determined impurity parameters are in satisfactory agreement with the observations from scanning tunneling microscopy (STM) experiments even in subtle details

Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Quantum secret sharing between multi-party and multi-party without entanglement

We propose a quantum secret sharing protocol between multi-party ($m$ members in group 1) and multi-party ($n$ members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations, then the last one (the $m^{th}$ member of group 1) sends $1/n$ of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.Comment: 6 pages, no figur

Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism

A method is presented for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy, i.e.\ materials such that $c_{ijkl}= c_{ijkl}(r)$ in a spherical coordinate system ${r,\theta,\phi}$. The time harmonic displacement field $\mathbf{u}(r,\theta ,\phi)$ is expanded in a separation of variables form with dependence on $\theta,\phi$ described by vector spherical harmonics with $r$-dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as $\mathbf{u}(r,\theta)$, admit this type of separation of variables solutions for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.Comment: 15 page

Pericentromeric heterochromatin is hierarchically organized and spatially contacts H3K9me2 islands in euchromatin.

Membraneless pericentromeric heterochromatin (PCH) domains play vital roles in chromosome dynamics and genome stability. However, our current understanding of 3D genome organization does not include PCH domains because of technical challenges associated with repetitive sequences enriched in PCH genomic regions. We investigated the 3D architecture of Drosophila melanogaster PCH domains and their spatial associations with the euchromatic genome by developing a novel analysis method that incorporates genome-wide Hi-C reads originating from PCH DNA. Combined with cytogenetic analysis, we reveal a hierarchical organization of the PCH domains into distinct territories. Strikingly, H3K9me2-enriched regions embedded in the euchromatic genome show prevalent 3D interactions with the PCH domain. These spatial contacts require H3K9me2 enrichment, are likely mediated by liquid-liquid phase separation, and may influence organismal fitness. Our findings have important implications for how PCH architecture influences the function and evolution of both repetitive heterochromatin and the gene-rich euchromatin