The distribution of forces affects vibrational properties in hard sphere glasses

We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{\theta_e}$ the force distribution of such pairs and $\phi_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $\omega^*$, rising up to it as $D(\omega) \sim \omega^{2+a}$, and decaying above $\omega^*$ as $D(\omega)\sim \omega^{-a}$ where $a=(1-\theta_e)/(3+\theta_e)$ and $\omega$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\langle \delta R^2\rangle\sim1/\mu\sim (\phi_c-\phi)^{\kappa}$ where $\kappa=2-2/(3+\theta_e)$, and (iii) continuum elasticity breaks down on a scale $\ell_c \sim1/\sqrt{\delta z}\sim (\phi_c-\phi)^{-b}$ where $b=(1+\theta_e)/(6+2\theta_e)$ and $\delta z=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $\theta_e\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $\kappa\approx1.41$, $a \approx 0.17$, and $b\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\infty$, whereas some observations differ, as rationalized by the present approach.Comment: 5 pages + 4 pages supplementary informatio

A Genetic Locus Regulates the Expression of Tissue-Specific mRNAs from Multiple Transcription Units

129 GIX- mice, unlike animals of the congeneic partner strain GIX+, do not express significant amounts of the retroviral antigens gp70 and p30. Evidence is presented indicating that the GIX phenotype is specified by a distinct regulatory gene acting on multiple transcription units to control the levels of accumulation of specific mRNA species. The steady-state levels of retroviral-homologous mRNA from the tissues of GIX+ and GIX- mice were examined by blot hybridization using as probes DNA fragments from cloned murine leukemia viruses. RNA potentially encoding viral antigens was reduced or absent in GIX- mice, even though no differences in integrated viral genomes were detected between these congeneic strains by DNA blotting. Tissue-specific patterns of accumulation of these RNA species were detected in brain, epididymis, liver, spleen, and thymus, and several distinct RNA species were found to be coordinately regulated with the GIX phenotype. Measurements of RNA synthesis suggest a major role for transcriptional control in the regulation of some retroviral messages

Theoretical considerations of some nonlinear aspects of hypersonic panel flutter Annual report, 1 Sep. 1967 - 31 Aug. 1968

Stability and postcritical response of infinite width panels on hinged supports due to aerodynamic loads at hypersonic spee

Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.Comment: 4 pages, 2 figure

Thermal noise and dephasing due to electron interactions in non-trivial geometries

We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.Comment: 9 pages, 6 figures (version submitted to PRB

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]

The quantization of phase is still an open problem. In the approach of Susskind and Glogower so called cosine and sine operators play a fundamental role. Their eigenstates in the Fock representation are related with the Chebyshev polynomials of the second kind. Here we introduce more general cosine and sine operators whose eigenfunctions in the Fock basis are related in a similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1]. To each polynomial set defined in terms of a weight function there corresponds a pair of cosine and sine operators. Depending on the symmetry of the weight function we distinguish generalized or extended operators. Their eigenstates are used to define cosine and sine representations and probability distributions. We consider also the inverse arccosine and arcsine operators and use their eigenstates to define cosine-phase and sine-phase distributions, respectively. Specific, numerical and graphical results are given for the classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure

Measuring Light Pollution with Fisheye Lens Imagery from A Moving Boat, A Proof of Concept

Near all-sky imaging photometry was performed from a boat on the Gulf of Aqaba to measure the night sky brightness in a coastal environment. The boat was not anchored, and therefore drifted and rocked. The camera was mounted on a tripod without any inertia/motion stabilization. A commercial digital single lens reflex (DSLR) camera and fisheye lens were used with ISO setting of 6400, with the exposure time varied between 0.5 s and 5 s. We find that despite movement of the vessel the measurements produce quantitatively comparable results apart from saturation effects. We discuss the potential and limitations of this method for mapping light pollution in marine and freshwater systems. This work represents the proof of concept that all-sky photometry with a commercial DSLR camera is a viable tool to determine light pollution in an ecological context from a moving boat.Comment: 9 pages, 6 figures, accepted at International Journal of Sustainable Lightin