Testing Cluster Structure of Graphs

We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if it can be partitioned into no more than $k$ parts, such that the (inner) conductance of the induced subgraph on each part is at least $\phi$ and the (outer) conductance of each part is at most $c_{d,k}\varepsilon^4\phi^2$, where $c_{d,k}$ depends only on $d,k$. Our main result is a sublinear algorithm with the running time $\widetilde{O}(\sqrt{n}\cdot\mathrm{poly}(\phi,k,1/\varepsilon))$ that takes as input a graph with maximum degree bounded by $d$, parameters $k$, $\phi$, $\varepsilon$, and with probability at least $\frac23$, accepts the graph if it is $(k,\phi)$-clusterable and rejects the graph if it is $\varepsilon$-far from $(k, \phi^*)$-clusterable for $\phi^* = c'_{d,k}\frac{\phi^2 \varepsilon^4}{\log n}$, where $c'_{d,k}$ depends only on $d,k$. By the lower bound of $\Omega(\sqrt{n})$ on the number of queries needed for testing graph expansion, which corresponds to $k=1$ in our problem, our algorithm is asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201

Development of a rotary fluid transfer coupling and support mechanism for space station

A design was developed for a rotary fluid coupling to transfer coolant fluids (primarily anhydrous ammonia) across rotating joints of the space station. Development testing using three conceptual designs yielded data which were used to establish the design of a multipass fluid coupling capable of handling three fluid circuits. In addition, a mechanism to support the fluid coupling and allow an astronaut to replace the coupling quickly and easily was designed

A Classical Molecular Dynamics Study on the Effect of Si/Al Ratio and Silanol Nest Defects on Water Diffusion in Zeolite HY

The diffusion of water confined in zeolite HY has been studied using classical molecular dynamics at 300 K to probe the effects of water loading, Si/Al ratio, and silanol nest defect presence on the behavior of water confined in Brønsted acidic faujasite (FAU) zeolites. Water loading, ranging from 5 to 33 wt %, is shown to have a significant effect on diffusivity, showing an increase by a factor of ∼7 over the loading range, toward a maximum diffusivity. Upon probing the effect of Si/Al ratio (in a range of Si/Al = 5 to fully siliceous), water diffusivity tends to decrease with the concentration of Brønsted acid sites which show strong interactions with the water molecules and thus hinder molecular mobility. The average residence time of water adsorbed to each Brønsted acid site also decreased with both water loading and Si/Al ratio. Water diffusivity shows the highest dependency on Si/Al ratio at 18 wt % loading, as a lack of total mobility in the systems at the lowest loadings is observed (due to significant populations of water molecules being immobilized via interaction with the framework and Brønsted acid sites), and less of a dependence is observed at the highest loadings due to the prevalence of sorbate-sorbate interactions. Notably, silanol nest presence (at a concentration of 1 per unit cell) had no significant effect on the diffusivity of water in HY at any water loading or Si/Al ratio. Reasons considered for this lack of influence include silanol geometry and flexibility at ambient temperature and potentially a lower effective charge density of the defect site.</p

A Classical Molecular Dynamics Study on the Effect of Si/Al Ratio and Silanol Nest Defects on Water Diffusion in Zeolite HY

The diffusion of water confined in zeolite HY has been studied using classical molecular dynamics at 300 K to probe the effects of water loading, Si/Al ratio, and silanol nest defect presence on the behavior of water confined in Brønsted acidic faujasite (FAU) zeolites. Water loading, ranging from 5 to 33 wt %, is shown to have a significant effect on diffusivity, showing an increase by a factor of ∼7 over the loading range, toward a maximum diffusivity. Upon probing the effect of Si/Al ratio (in a range of Si/Al = 5 to fully siliceous), water diffusivity tends to decrease with the concentration of Brønsted acid sites which show strong interactions with the water molecules and thus hinder molecular mobility. The average residence time of water adsorbed to each Brønsted acid site also decreased with both water loading and Si/Al ratio. Water diffusivity shows the highest dependency on Si/Al ratio at 18 wt % loading, as a lack of total mobility in the systems at the lowest loadings is observed (due to significant populations of water molecules being immobilized via interaction with the framework and Brønsted acid sites), and less of a dependence is observed at the highest loadings due to the prevalence of sorbate-sorbate interactions. Notably, silanol nest presence (at a concentration of 1 per unit cell) had no significant effect on the diffusivity of water in HY at any water loading or Si/Al ratio. Reasons considered for this lack of influence include silanol geometry and flexibility at ambient temperature and potentially a lower effective charge density of the defect site.</p

Customer mobility and congestion in supermarkets

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intra-city scales to inter-country scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65--70\% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than a supermarket's original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales

Inertial range scaling in numerical turbulence with hyperviscosity

Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case--presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t^{-1.25} decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong.Comment: Final version (7 pages

Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice

The Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice is investigated. We show that the effective mass increases in an optical superlattice, which leads to localization of the BEC, in accordance with recent experimental observations [16]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.Comment: Modified manuscrip

Level density for deformations of the Gaussian orthogonal ensemble

Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to $m$ GOEs.Comment: 7 pages revtex4, 5 eps figures, submitted to Phys. Rev.

Phonon density of states and heat capacity of La_(3−x)Te_4

The phonon density of states (DOS) of La_(3−x)Te_4 compounds (x=0.0,0.18,0.32) was measured at 300, 520, and 780 K, using inelastic neutron scattering. A significant stiffening of the phonon DOS and a large broadening of features were observed upon introduction of vacancies on La sites (increasing x). Heat-capacity measurements were performed at temperatures 1.85 ≤ T ≤ 1200 K and were analyzed to quantify the contributions of phonons and electrons. The Debye temperature and the electronic coefficient of heat capacity determined from these measurements are consistent with the neutron-scattering results, and with previously reported first-principles calculations. Our results indicate that La vacancies in La_(3−x)Te_4 strongly scatter phonons and this source of scattering appears to be independent of temperature. The stiffening of the phonon DOS induced by the introduction of vacancies is explained in terms of the electronic structure and the change in bonding character. The temperature dependence of the phonon DOS is captured satisfactorily by the quasiharmonic approximation