Reentrant Adhesion Behavior in Nanocluster Deposition

We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft-landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of incident kinetic energy, we find a transition from adhesion to reflection at low kinetic energies. We also identify a second adhesive regime at intermediate kinetic energies, where strong deformation of the cluster leads to an increase in contact area and adhesive energy.Comment: 7 pages, 6 figure

Phase transitions in Lu2_2Ir3_3Si5_5

We report the results of our investigations on a polycrystalline sample of Lu$_2$Ir$_3$Si$_5$ which crystallizes in the U$_2$Co$_3$Si$_5$ type structure (Ibam). These investigations comprise powder X-ray diffraction, magnetic susceptibility, electrical resistivity and high temperature (120-300 K) heat capacity studies. Our results reveal that the sample undergoes a superconducting transition below 3.5 K. It also undergoes a first order phase transition between 150-250 K as revealed by an upturn in the resistivity, a diasmagnetic drop in the magnetic susceptibility and a large anomaly (20-30 J/mol K) in the specific heat data. We observe a huge thermal hysteresis of almost 45 K between the cooling and warming data across this high temperature transition in all our measurements. Low temperature X-ray diffraction measurements at 87 K reveals that the compound undergoes a structural change at the high temperature transition. Resistivity data taken in repeated cooling and warming cycles indicate that at the high temperature transition, the system goes into a highly metastable state and successive heating/cooling curves are found to lie above the previous one and the resistance keeps increasing with every thermal cycle. The room temperature resistance of a thermaly cycled piece of the sample decays exponentialy with time with a decay time constant estimated to be about 10$^4$ secs. The anomaly (upturn) in the resistivity and the large drop (almost 45%) in the susceptibility across the high temperature transition suggest that the observed structural change is accompanied or induced by an electronic transition.Comment: 7 figures, 1 table and 18 reference

Molecular dynamics simulations of reflection and adhesion behavior in Lennard-Jones cluster deposition

We conduct molecular dynamics simulations of the collision of atomic clusters with a weakly-attractive surface. We focus on an intermediate regime, between soft-landing and fragmentation, where the cluster undergoes deformation on impact but remains largely intact, and will either adhere to the surface (and possibly slide), or be reflected. We find that the outcome of the collision is determined by the Weber number, We i.e. the ratio of the kinetic energy to the adhesion energy, with a transition between adhesion and reflection occurring as We passes through unity. We also identify two distinct collision regimes: in one regime the collision is largely elastic and deformation of the cluster is relatively small but in the second regime the deformation is large and the adhesion energy starts to depend on the kinetic energy. If the transition between these two regimes occurs at a similar kinetic energy to that of the transition between reflection and adhesion, then we find that the probability of adhesion for a cluster can be bimodal. In addition we investigate the effects of the angle of incidence on adhesion and reflection. Finally we compare our findings both with recent experimental results and with macroscopic theories of particle collisions.Comment: 18 pages, 13 figure

Relax, no need to round: integrality of clustering formulations

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and (b) they are generic tools which are relatively parameter-free, not tailored to specific assumptions over the input. More precisely, we consider the distributional setting where there are $k$ clusters in $\mathbb{R}^m$ and data from each cluster consists of $n$ points sampled from a symmetric distribution within a ball of unit radius. We ask: what is the minimal separation distance between cluster centers needed for convex relaxations to exactly recover these $k$ clusters as the optimal integral solution? For the $k$-median linear programming relaxation we show a tight bound: exact recovery is obtained given arbitrarily small pairwise separation $\epsilon > 0$ between the balls. In other words, the pairwise center separation is $\Delta > 2+\epsilon$. Under the same distributional model, the $k$-means LP relaxation fails to recover such clusters at separation as large as $\Delta = 4$. Yet, if we enforce PSD constraints on the $k$-means LP, we get exact cluster recovery at center separation $\Delta > 2\sqrt2(1+\sqrt{1/m})$. In contrast, common heuristics such as Lloyd's algorithm (a.k.a. the $k$-means algorithm) can fail to recover clusters in this setting; even with arbitrarily large cluster separation, k-means++ with overseeding by any constant factor fails with high probability at exact cluster recovery. To complement the theoretical analysis, we provide an experimental study of the recovery guarantees for these various methods, and discuss several open problems which these experiments suggest.Comment: 30 pages, ITCS 201