Nonlinear Energy Response of Glass Forming Materials

A theory for the nonlinear energy response of a system subjected to a heat bath is developed when the temperature of the heat bath is modulated sinusoidally. The theory is applied to a model glass forming system, where the landscape is assumed to have 20 basins and transition rates between basins obey a power law distribution. It is shown that the statistics of eigenvalues of the transition rate matrix, the glass transition temperature $T_g$, the Vogel-Fulcher temperature $T_0$ and the crossover temperature $T_x$ can be determined from the 1st- and 2nd-order ac specific heats, which are defined as coefficients of the 1st- and 2nd-order energy responses. The imaginary part of the 1st-order ac specific heat has a broad peak corresponding to the distribution of the eigenvalues. When the temperature is decreased below $T_g$, the frequency of the peak decreases and the width increases. Furthermore, the statistics of eigenvalues can be obtained from the frequency dependence of the 1st-order ac specific heat. The 2nd-order ac specific heat shows extrema as a function of the frequency. The extrema diverge at the Vogel-Fulcher temperature $T_0$. The temperature dependence of the extrema changes significantly near $T_g$ and some extrema vanish near $T_x$.Comment: 20 pages, 10 figure

Distributed Agreement on Activity Driven Networks

In this paper, we investigate asymptotic properties of a consensus protocol taking place in a class of temporal (i.e., time-varying) networks called the activity driven network. We first show that a standard methodology provides us with an estimate of the convergence rate toward the consensus, in terms of the eigenvalues of a matrix whose computational cost grows exponentially fast in the number of nodes in the network. To overcome this difficulty, we then derive alternative bounds involving the eigenvalues of a matrix that is easy to compute. Our analysis covers the regimes of 1) sparse networks and 2) fast-switching networks. We numerically confirm our theoretical results by numerical simulations

Mergers of accreting stellar-mass black holes

We present post-Newtonian $N$-body simulations on mergers of accreting stellar-mass black holes (BHs), where such general relativistic effects as the pericenter shift and gravitational wave (GW) emission are taken into consideration. The attention is concentrated on the effects of the dynamical friction and the Hoyle-Lyttleton mass accretion by ambient gas. We consider a system composed of ten BHs with initial mass of $30~M_\odot$. As a result, we show that mergers of accreting stellar-mass BHs are classified into four types: a gas drag-driven, an interplay-driven, a three body-driven, or an accretion-driven merger. We find that BH mergers proceed before significant mass accretion, even if the accretion rate is $\sim10$ Eddington accretion rate, and then all BHs can merge into one heavy BH. Using the simulation results for a wide range of parameters, we derive a critical accretion rate ($\dot{m}_{\rm c}$), below which the BH growth is promoted faster by mergers. Also, it is found that the effect of the recoil by the GW emission can reduce $\dot{m}_{\rm c}$ especially in gas number density higher than $10^8~{\rm cm}^{-3}$, and enhance the escape probability of merged BHs. Very recently, a gravitational wave event, GW150914, as a result of the merger of a $\sim 30~M_\odot$ BH binary has been detected (Abbott et al. 2016). Based on the present simulations, the BH merger in GW150914 is likely to be driven by three-body encounters accompanied by a few $M_\odot$ of gas accretion, in high-density environments like dense interstellar clouds or galactic nuclei.Comment: 13 pages, 16 figures. Accepted for publication in MNRA

A q-analogue of Catalan Hankel determinants

In this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers. Here we consider $\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a q-analogue of Catalan numbers $C_{n}=\frac1{n+1}\binom{2n}{n}$, which is known as the moments of the little q-Jacobi polynomials. We also give several proofs of this q-analogue, in which we use lattice paths, the orthogonal polynomials, or the basic hypergeometric series. We also consider a q-analogue of Schr\"oder Hankel determinants, and give a new proof of Moztkin Hankel determinants using an addition formula for ${}_2F_{1}$.Comment: 17 page

Microdroplet impact at very high velocity

Water microdroplet impact at velocities up to 100 m/s for droplet diameters from 12 to 100 um is studied. This parameter range covers the transition from capillary-limited to viscosity-limited spreading of the impacting droplet. Splashing is absent for all measurements; the droplets always gently spread over the surface. The maximum spreading radius is compared to several existing models. The model by Pasandideh-Fard et al. agrees well with the measured data, indicating the importance of a thin boundary layer just above the surface, in which most of the viscous dissipation in the spreading droplet takes place. As explained by the initial air layer under the impacting droplet, a contact angle of 180 degrees is used as model input

Dissociation Dynamics of CIONO_2 and Relative Cl and ClO Product Yields following Photoexcitation at 308 nm

Chlorine nitrate photolysis at 308 nm has been investigated with a molecular beam technique. Two primary decomposition pathways, leading to Cl + NO_3 and ClO + NO_2, were observed. The branching ratio between these two respective channels was determined to be 0.67 ± 0.06 : 0.33 ± 0.06. This ratio is an upper limit because some of the ClO photoproducts may have undergone secondary photodissociation. The angular distributions of the photoproducts with respect to the direction of polarization of the exciting light were anisotropic. The anisotropy parameters were β= 0.5 ± 0.2 for the Cl + NO_3 channel and β= 1.1 ± 0.2 for the ClO + NO_2 channel, indicating that dissociation of ClONO_2 by either pathway occurs within a rotational period. Weak signal at mass-to-charge ratios of 35 and 51, arising from products with laboratory velocities close to the beam velocity, was observed. While this signal could result from statistical dissociation channels with a total relative yield of 0.07 or less, it is more likely attributable to products from ClO secondary photodissociation or from dissociation of clusters