Angular Normal Modes of a Circular Coulomb Cluster

We investigate the angular normal modes for small oscillations about an equilibrium of a single-component coulomb cluster confined by a radially symmetric external potential to a circle. The dynamical matrix for this system is a Laplacian symmetrically circulant matrix and this result leads to an analytic solution for the eigenfrequencies of the angular normal modes. We also show the limiting dependence of the largest eigenfrequency for large numbers of particles

Specific volumes of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy in the liquid, glass, and crystalline states

The specific volumes of the Zr41.2Ti13.8CU12.5Ni10.0Be2.25 alloy as a function of temperature, T, are determined by employing an image digitizing technique and numerical calculation methods applied to the electrostatically levitated spherical alloy. The linear fitting of the volumes of the alloy in the liquid, V-l, glass, V-g, and crystalline V-c, states in the temperature ranges shown in parentheses are V-l(T) = 0.1583 + 8.877 x 10(-6)T(cm^(3)/g) (700-1300 K); V-g(T) = 0.1603 + 5.528 x 10^(-6)T (400-550 K); V-c(T) = 0.1583 + 6.211 x 10(-6)T(400-850 K). The average volume thermal expansion coefficients within the temperature ranges are determined to be 5.32, 3.39, and 3.83 x 10^(-5) (1/K) for the liquid, glass, and crystalline states, respectively

Quintessential Kination and Leptogenesis

Thermal leptogenesis induced by the CP-violating decay of a right-handed neutrino (RHN) is discussed in the background of quintessential kination, i.e., in a cosmological model where the energy density of the early Universe is assumed to be dominated by the kinetic term of a quintessence field during some epoch of its evolution. This assumption may lead to very different observational consequences compared to the case of a standard cosmology where the energy density of the Universe is dominated by radiation. We show that, depending on the choice of the temperature T_r above which kination dominates over radiation, any situation between the strong and the super--weak wash--out regime are equally viable for leptogenesis, even with the RHN Yukawa coupling fixed to provide the observed atmospheric neutrino mass scale ~ 0.05 eV. For M< T_r < M/100, i.e., when kination stops to dominate at a time which is not much later than when leptogenesis takes place, the efficiency of the process, defined as the ratio between the produced lepton asymmetry and the amount of CP violation in the RHN decay, can be larger than in the standard scenario of radiation domination. This possibility is limited to the case when the neutrino mass scale is larger than about 0.01 eV. The super--weak wash--out regime is obtained for T_r << M/100, and includes the case when T_r is close to the nucleosynthesis temperature ~ 1 MeV. Irrespective of T_r, we always find a sufficient window above the electroweak temperature T ~ 100 GeV for the sphaleron transition to thermalize, so that the lepton asymmetry can always be converted to the observed baryon asymmetry.Comment: 13 pages, 8 figure

Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. For the first time we report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$ and examine the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles, by measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near $\nu=5/2$ and $7/2$, indicating stability of the fermion parity. When phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with fermion parity change. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.Comment: A significantly revised version; 54 double-column pages containing 14 pages of main text + Supplementary Materials. The figures, which include a number of new figures, are now incorporated into the tex

Peeling from a patterned thin elastic film

Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack initiation from an incision on the film occurs at a load much higher than that required to propagate it on a smooth adhesive surface; multiple incisions thus cause the crack to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of cavitation bubbles behind the incision which must grow and coalesce before a viable crack propagates. Our theoretical analysis allows us to rationalize these experimental observations qualitatively and quantitatively and suggests a simple design criterion for increasing the interfacial fracture toughness of adhesive films.Comment: 8 pages, To appear in Proceedings of Royal Society London, Ser.

Quantum phase transitions in a resonant-level model with dissipation: Renormalization-group studies

We study a spinless level that hybridizes with a fermionic band and is also coupled via its charge to a dissipative bosonic bath. We consider the general case of a power-law hybridization function \Gamma(\w)\propto |\w|^r with $r\ge 0$, and a bosonic bath spectral function B(\w)\propto \w^s with $s\ge -1$. For $r<1$ and $\mathrm{max}(0,2r-1)<s<1$, this Bose-Fermi quantum impurity model features a continuous zero-temperature transition between a delocalized phase, with tunneling between the impurity level and the band, and a localized phase, in which dissipation suppresses tunneling in the low-energy limit. The phase diagram and the critical behavior of the model are elucidated using perturbative and numerical renormalization-group techniques, between which there is excellent agreement in the appropriate regimes. For $r=0$ this model's critical properties coincide with those of the spin-boson and Ising Bose-Fermi Kondo models, as expected from bosonization.Comment: 14 pages, 14 eps figure

Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

Random Vibrational Networks and Renormalization Group

We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several real-space renormalization techniques which can be used to describe this dynamics on general networks, drawing on strong disorder techniques developed for regular lattices. The renormalization group is capable of elucidating the localization properties, and provides, even for specific network instances, a fast approximation technique for determining the spectra which compares well with exact results.Comment: 4 pages, 3 figure