Gravity-modes in ZZ Ceti Stars. II. Effects of Turbulent Dissipation

We investigate dynamical interactions between turbulent convection and g-mode pulsations in ZZ Ceti variables (DAVs). Since our understanding of turbulence is rudimentary, we are compelled to settle for order of magnitude results. A key feature of these interactions is that convective response times are much shorter than pulsation periods. Thus the dynamical interactions enforce near uniform horizontal velocity inside the convection zone. They also give rise to a narrow shear layer in the region of convective overshoot at the top of the radiative interior. Turbulent damping inside the convection zone is negligible for all modes, but that in the region of convective overshoot may be significant for a few long period modes near the red edge of the instability strip. These conclusions are in accord with those reached earlier by Brickhill. Our major new result concerns nonlinear damping arising from the Kelvin-Helmholtz instability of the aforementioned shear layer. Amplitudes of overstable modes saturate where dissipation due to this instability balances excitation by convective driving. This mechanism of amplitude saturation is most effective for long period modes, and it may play an important role in defining the red edge of the instability strip.Comment: 7 pages, including 2 figures. Used emulateapj.sty and apjfonts.sty obtained from http://hea-www.harvard.edu/~alexey/emulateapj

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

The Range of Topological Effects on Communication

We continue the study of communication cost of computing functions when inputs are distributed among $k$ processors, each of which is located at one vertex of a network/graph called a terminal. Every other node of the network also has a processor, with no input. The communication is point-to-point and the cost is the total number of bits exchanged by the protocol, in the worst case, on all edges. Chattopadhyay, Radhakrishnan and Rudra (FOCS'14) recently initiated a study of the effect of topology of the network on the total communication cost using tools from $L_1$ embeddings. Their techniques provided tight bounds for simple functions like Element-Distinctness (ED), which depend on the 1-median of the graph. This work addresses two other kinds of natural functions. We show that for a large class of natural functions like Set-Disjointness the communication cost is essentially $n$ times the cost of the optimal Steiner tree connecting the terminals. Further, we show for natural composed functions like $\text{ED} \circ \text{XOR}$ and $\text{XOR} \circ \text{ED}$, the naive protocols suggested by their definition is optimal for general networks. Interestingly, the bounds for these functions depend on more involved topological parameters that are a combination of Steiner tree and 1-median costs. To obtain our results, we use some new tools in addition to ones used in Chattopadhyay et. al. These include (i) viewing the communication constraints via a linear program; (ii) using tools from the theory of tree embeddings to prove topology sensitive direct sum results that handle the case of composed functions and (iii) representing the communication constraints of certain problems as a family of collection of multiway cuts, where each multiway cut simulates the hardness of computing the function on the star topology

Simulating Star Formation and Feedback in Galactic Disk Models

We use a high-resolution grid-based hydrodynamics method to simulate the multi-phase interstellar medium in a Milky Way-size quiescent disk galaxy. The models are global and three-dimensional, and include a treatment of star formation and feedback. We examine the formation of gravitational instabilities and show that a form of the Toomre instability criterion can successfully predict where star formation will occur. Two common prescriptions for star formation are investigated. The first is based on cosmological simulations and has a relatively low threshold for star formation, but also enforces a comparatively low efficiency. The second only permits star formation above a number density of 1000 cm^-3 but adopts a high efficiency. We show that both methods can reproduce the observed slope of the relationship between star formation and gas surface density (although at too high a rate for our adopted parameters). A run which includes feedback from type II supernovae is successful at driving gas out of the plane, most of which falls back onto the disk. This feedback also substantially reduces the star formation rate. Finally, we examine the density and pressure distribution of the ISM, and show that there is a rough pressure equilibrium in the disk, but with a wide range of pressures at a given location (and even wider for the case including feedbackComment: 14 pages, 12 figures, accepted to Astrophysical Journa

When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the $n$-stage repeated version of the game exist if and only if both players have $\Omega(n)$ random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the $n$-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on "random-like" sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then $\Omega(n)$ random bits remain necessary for equilibria to exist

Magnetospheric eclipses in the double pulsar system J0737-3039

We argue that eclipses of radio emission from the millisecond pulsar A in the double pulsar system J0737-3039 are due to synchrotron absorption by plasma in the closed field line region of the magnetosphere of its normal pulsar companion B. A's radio beam only illuminates B's magnetosphere for about 10 minutes surrounding the time of eclipse. During this time it heats particles at r\gtrsim 10^9 cm to relativistic energies and enables extra plasma to be trapped by magnetic mirroring. An enhancement of the plasma density by a factor \sim 10^2 is required to match the duration and optical depth of the observed eclipses. The extra plasma might be supplied by a source near B through B\gamma pair creation by energetic photons produced in B's outer gap. Excitation of pairs' gyrational motions by cyclotron absorption of A's radio beam can result in their becoming trapped between conjugate mirror points in B's magnetosphere. Because the trapping efficiency decreases with increasing optical depth, the plasma density enhancement saturates even under steady state illumination. The result is an eclipse with finite, frequency dependent, optical depth. After illumination by A's radio beam ceases, the trapped particles cool and are lost. The entire cycle repeats every orbital period. We speculate that the asymmetries between eclipse ingress and egress result in part from the magnetosphere's evolution toward a steady state when illuminated by A's radio beam. We predict that A's linear polarization will vary with both eclipse phase and B's rotational phase.Comment: 8 pages, 1 figure, submitted to ApJ, references corrected, detectability of reprocessed emission revised, major conclusions unchange

Excitation of stellar p-modes by turbulent convection : 2. The Sun

Acoustic power and oscillation amplitudes of radial oscillations computed for a solar model are compared with solar seismic observations. The oscillations are assumed stochastically excited by turbulence. The numerical computations are based upon a theoretical formulation of the power going into solar like oscillation modes as proposed by Samadi et al. (2000) in a companion paper. This formulation allows to investigate several assumptions concerning properties of the stellar turbulence. We find that the entropy source plays a dominant role in the stochastic excitation compared with the Reynold stress source in agreement with Goldreich et al. (1994). We consider several turbulent kinetic energy spectra suggested by different observations of the solar granulation. Differences between turbulent spectra manifest themselves by large differences in the computed oscillation powers at high oscillation frequency. Two free parameters which are introduced in the description of the turbulence enter the expression for the acoustic power. These parameters are adjusted in order to fit to the solar observations of the surface velocity oscillations. The best fit is obtained with the kinetic energy spectrum deduced from the observations of the solar granulation by Nesis et al. (1993); the corresponding adjusted parameters are found to be compatible with the theoretical upper limit which can be set on these parameters. The adopted theoretical approach improves the agreement between solar seismic observations and numerical results.Comment: 11 pages, 11 figures, accepted for publication in A&

Data-Oblivious Graph Algorithms in Outsourced External Memory

Motivated by privacy preservation for outsourced data, data-oblivious external memory is a computational framework where a client performs computations on data stored at a semi-trusted server in a way that does not reveal her data to the server. This approach facilitates collaboration and reliability over traditional frameworks, and it provides privacy protection, even though the server has full access to the data and he can monitor how it is accessed by the client. The challenge is that even if data is encrypted, the server can learn information based on the client data access pattern; hence, access patterns must also be obfuscated. We investigate privacy-preserving algorithms for outsourced external memory that are based on the use of data-oblivious algorithms, that is, algorithms where each possible sequence of data accesses is independent of the data values. We give new efficient data-oblivious algorithms in the outsourced external memory model for a number of fundamental graph problems. Our results include new data-oblivious external-memory methods for constructing minimum spanning trees, performing various traversals on rooted trees, answering least common ancestor queries on trees, computing biconnected components, and forming open ear decompositions. None of our algorithms make use of constant-time random oracles.Comment: 20 page