Search for: All records

We study the linear stability of a compressible sessile bubble in an ambient fluid that partially wets a planar solid support, where the gas is assumed to be an ideal gas that obeys the adiabatic law. The frequency spectrum is computed from an integrodifferential boundary value problem and depends upon the wetting conditions through the static contact angle $\alpha$ , the dimensionless equilibrium bubble pressure $\varPi$ , and the contact-line dynamics that we assume to be either (i) pinned or (ii) freely moving with fixed contact angle. Corresponding mode shapes are defined by the polar-azimuthal mode number pair $[k,\ell ]$ with $k+\ell =\mathbb {Z}^{+}_{even}$ . We report instabilities to the (i) $[0,0]$ breathing mode associated with volume change, and (ii) $[1,1]$ mode that is linked to horizontal centre-of-mass motion of the bubble. Stability diagrams and instability growth rates are computed, and the respective instability mechanisms are revealed through an energy analysis. The zonal $\ell =0$ modes are associated with volume change, and we show that there is a complex dependence between the classical volume and shape change modes for wetting conditions that differ from neutral wetting $\alpha =90^\circ$ . Finally, we show how the classical frequency degeneracy for the Rayleigh–Lamb modes of the free bubble splits for the azimuthal modes $\ell \neq 0,1$ . 

Drop-on-demand printing applications involve a drop connected to a fluid reservoir between which volume can be exchanged, a situation that can be idealized as a sessile drop with prescribed volume flux across the drop/reservoir boundary. Here we compute the frequency spectrum for these pressure disturbances, as it depends upon the static contact-angle $\alpha$ (CA) and an empirical constant $\chi$ relating the reservoir pressure to volume exchanged, for either (i) pinned or (ii) free contact-lines. Mode shapes are characterized by the mode number pair $[k,\ell ]$ with property $k+\ell =\mathbb {Z}^{+}_{odd}$ that can be associated with the symmetry properties of the Rayleigh drop modes for the free sphere. We report instabilities to the axisymmetric $[1,0]$ and non-axisymmetric rocking $[2,1]$ modes that are related to centre-of-mass motions, and show how the spectral degeneracy of the Rayleigh drop modes breaks with the model parameters. 

We consider the distributed statistical learning problem in a high-dimensional adversarial scenario. At each iteration, $m$ worker machines compute stochastic gradients and send them to a master machine. However, an $\alpha$-fraction of $m$ worker machines, called Byzantine machines, may act adversarially and send faulty gradients. To guard against faulty information sharing, we develop a distributed robust learning algorithm based on Nesterov's dual averaging. This algorithms is provably robust against Byzantine machines whenever $\alpha\in[0, 1/2)$. For smooth convex functions, we show that running the proposed algorithm for $T$ iterations achieves a statistical error bound $\tilde{O}\big(1/\sqrt{mT}+\alpha/\sqrt{T}\big)$. This result holds for a large class of normed spaces and it matches the known statistical error bound for Byzantine stochastic gradient in the Euclidean space setting. A key feature of the algorithm is that the dimension dependence of the bound scales with the dual norm of the gradient; in particular, for probability simplex, we show that it depends logarithmically on the problem dimension $d$. Such a weak dependence on the dimension is desirable in high-dimensional statistical learning and it has been known to hold for the classical mirror descent but it appears to be new for the Byzantine gradient scenario. 

We study a distributed policy evaluation problem in which a group of agents with jointly observed states and private local actions and rewards collaborate to learn the value function of a given policy via local computation and communication. This problem arises in various large-scale multi-agent systems, including power grids, intelligent transportation systems, wireless sensor networks, and multi-agent robotics. We develop and analyze a new distributed temporal-difference learning algorithm that minimizes the mean-square projected Bellman error. Our approach is based on a stochastic primal-dual method and we improve the best-known convergence rate from $O(1/\sqrt{T})$ to $O(1/T)$, where $T$ is the total number of iterations. Our analysis explicitly takes into account the Markovian nature of the sampling and addresses a broader class of problems than the commonly-used i.i.d. sampling scenario. 

The superτ-charm facility (STCF) is an electron–positron collider proposed by the Chinese particle physics community. It is designed to operate in a center-of-mass energy range from 2 to 7 GeV with a peak luminosity of 0.5 × 10³⁵cm⁻²·s⁻¹or higher. The STCF will produce a data sample about a factor of 100 larger than that of the presentτ-charm factory — the BEPCII, providing a unique platform for exploring the asymmetry of matter-antimatter (charge-parity violation), in-depth studies of the internal structure of hadrons and the nature of non-perturbative strong interactions, as well as searching for exotic hadrons and physics beyond the Standard Model. The STCF project in China is under development with an extensive R&D program. This document presents the physics opportunities at the STCF, describes conceptual designs of the STCF detector system, and discusses future plans for detector R&D and physics case studies.