Electrohydrodynamically induced mixing in immiscible multilayer flows

In the present study we investigate electrostatic stabilization mechanisms acting on stratified fluids. Electric fields have been shown to control and even suppress the Rayleigh-Taylor instability when a heavy fluid lies above lighter fluid. From a different perspective, similar techniques can also be used to generate interfacial dynamics in otherwise stable systems. We aim to identify active control protocols in confined geometries that induce time dependent flows in small scale devices without having moving parts. This effect has numerous applications, ranging from mixing phenomena to electric lithography. Two-dimensional computations are carried out and several such protocols are described. We present computational fluid dynamics videos with different underlying mixing strategies, which show promising results.Comment: Video submission for the gallery of fluid motion, as part of the APS DFD 2013 conferenc

Solid-solid phase transition in hard ellipsoids

We present a computer simulation study of the crystalline phases of hard ellipsoids of revolution. A previous study [Phys. Rev. E, \textbf{75}, 020402 (2007)] showed that for aspect ratios $a/b\ge 3$ the previously suggested stretched-fcc phase [Mol. Phys., \textbf{55}, 1171 (1985)] is unstable with respect to a simple monoclinic phase with two ellipsoids of different orientations per unit cell (SM2). In order to study the stability of these crystalline phases at different aspect ratios and as a function of density we have calculated their free energies by thermodynamic integration. The integration path was sampled by an expanded ensemble method in which the weights were adjusted by the Wang-Landau algorithm. We show that for aspect ratios $a/b\ge 2.0$ the SM2 structure is more stable than the stretched-fcc structure for all densities above solid-nematic coexistence. Between $a/b=1.55$ and $a/b=2.0$ our calculations reveal a solid-solid phase transition

Plane-extraction from depth-data using a Gaussian mixture regression model

We propose a novel algorithm for unsupervised extraction of piecewise planar models from depth-data. Among other applications, such models are a good way of enabling autonomous agents (robots, cars, drones, etc.) to effectively perceive their surroundings and to navigate in three dimensions. We propose to do this by fitting the data with a piecewise-linear Gaussian mixture regression model whose components are skewed over planes, making them flat in appearance rather than being ellipsoidal, by embedding an outlier-trimming process that is formally incorporated into the proposed expectation-maximization algorithm, and by selectively fusing contiguous, coplanar components. Part of our motivation is an attempt to estimate more accurate plane-extraction by allowing each model component to make use of all available data through probabilistic clustering. The algorithm is thoroughly evaluated against a standard benchmark and is shown to rank among the best of the existing state-of-the-art methods.Comment: 11 pages, 2 figures, 1 tabl

Instability and dripping of electrified liquid films flowing down inverted substrates

We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a nonzero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set up parallel to the substrate surface—this nonlocal physical mechanism has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films that are hanging from the underside of the substrate; these films may drip depending on physical parameters, and we investigate whether a sufficiently strong electric field can suppress such nonlinear phenomena. For a non-electrified flow, it was observed by Brun et al. [Phys. Fluids 27, 084107 (2015)] that the thresholds of linear absolute instability and dripping are reasonably close. In the present study, we incorporate an electric field and analyze the absolute and convective instabilities of a hierarchy of reduced-order models to predict the dripping limit in parameter space. The spatial stability results for the reduced-order models are verified by performing an impulse-response analysis with direct numerical simulations (DNS) of the Navier–Stokes equations coupled to the appropriate electrical equations. Guided by the results of the linear theory, we perform DNS on extended domains with inflow and outflow conditions (mimicking an experimental setup) to investigate the dripping limit for both non-electrified and electrified liquid films. For the latter, we find that the absolute instability threshold provides an order-of-magnitude estimate for the electric-field strength required to suppress dripping; the linear theory may thus be used to determine the feasibility of dripping suppression given a set of geometrical, fluid, and electrical parameters

Divergence of the Magnetic Gr\"{u}neisen Ratio at the Field-Induced Quantum Critical Point in YbRh2_2Si2_2

The heavy fermion compound YbRh$_2$Si$_2$ is studied by low-temperature magnetization $M(T)$ and specific-heat $C(T)$ measurements at magnetic fields close to the quantum critical point ($H_c=0.06$ T, $H\perp c$). Upon approaching the instability, $dM/dT$ is more singular than $C(T)$, leading to a divergence of the magnetic Gr\"uneisen ratio $\Gamma_{\rm mag}=-(dM/dT)/C$. Within the Fermi liquid regime, $\Gamma_{\rm mag}=-G_r(H-H_c^{fit})$ with $G_r=-0.30\pm 0.01$ and $H_c^{fit}=(0.065\pm 0.005)$ T which is consistent with scaling behavior of the specific-heat coefficient in YbRh$_2$(Si$_{0.95}$Ge$_{0.05}$)$_2$. The field-dependence of $dM/dT$ indicates an inflection point of the entropy as a function of magnetic field upon passing the line $T^\star(H)$ previously observed in Hall- and thermodynamic measurements.Comment: 4 pages, 3 Figure

Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels

Mobile communication channels are often modeled as linear time-varying filters or, equivalently, as time-frequency integral operators with finite support in time and frequency. Such a characterization inherently assumes the signals are narrowband and may not be appropriate for wideband signals. In this paper time-scale characterizations are examined that are useful in wideband time-varying channels, for which a time-scale integral operator is physically justifiable. A review of these time-frequency and time-scale characterizations is presented. Both the time-frequency and time-scale integral operators have a two-dimensional discrete characterization which motivates the design of time-frequency or time-scale rake receivers. These receivers have taps for both time and frequency (or time and scale) shifts of the transmitted signal. A general theory of these characterizations which generates, as specific cases, the discrete time-frequency and time-scale models is presented here. The interpretation of these models, namely, that they can be seen to arise from processing assumptions on the transmit and receive waveforms is discussed. Out of this discussion a third model arises: a frequency-scale continuous channel model with an associated discrete frequency-scale characterization.Comment: To appear in Communications in Information and Systems - special issue in honor of Thomas Kailath's seventieth birthda

Polarized neutron channeling as a tool for the investigations of weakly magnetic thin films

We present and apply a new method to measure directly weak magnetization in thin films. The polarization of a neutron beam channeling through a thin film structure is measured after exiting the structure edge as a microbeam. We have applied the method to a tri-layer thin film structure acting as a planar waveguide for polarized neutrons. The middle guiding layer is a rare earth based ferrimagnetic material TbCo5 with a low magnetization of about 20 mT. We demonstrate that the channeling method is more sensitive than the specular neutron reflection method

Thermodynamic behavior of the XXZ Heisenberg s=1/2 chain around the factorizing magnetic field

We have investigated the zero and finite temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h_f) and the critical one (h_c). The model presents a spin-flop phase for 0<h<h_f with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h=h_f. The entanglement estimators clearly show that the entanglement is lost exactly at h=h_f which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h=h_f) the ground state is known exactly as a product of single particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double peak structure is found in the specific heat around h=h_f which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.Comment: Will be published in JPCM (2010), 7 figure