Optimal Control of Uniformly Heated Granular Fluids in Linear Response

We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously—from a mathematical point of view—prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.

Benzohexacene guide in accurate determination of field effect carrier mobilities in long acenes

Four-probes mobility vs. VGS in the linear regime (VDS = −10 V) for benzohexacene based transistor.

On the Neural Tangent Kernel of Deep Networks with Orthogonal Initialization

The prevailing thinking is that orthogonal weights are crucial to enforcing dynamical isometry and speeding up training. The increase in learning speed that results from orthogonal initialization in linear networks has been well-proven. However, while the same is believed to also hold for nonlinear networks when the dynamical isometry condition is satisfied, the training dynamics behind this contention have not been thoroughly explored. In this work, we study the dynamics of ultra-wide networks across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural Networks (CNNs) with orthogonal initialization via neural tangent kernel (NTK). Through a series of propositions and lemmas, we prove that two NTKs, one corresponding to Gaussian weights and one to orthogonal weights, are equal when the network width is infinite. Further, during training, the NTK of an orthogonally-initialized infinite-width network should theoretically remain constant. This suggests that the orthogonal initialization cannot speed up training in the NTK (lazy training) regime, contrary to the prevailing thoughts. In order to explore under what circumstances can orthogonality accelerate training, we conduct a thorough empirical investigation outside the NTK regime. We find that when the hyper-parameters are set to achieve a linear regime in nonlinear activation, orthogonal initialization can improve the learning speed with a large learning rate or large depth.

Non-Linear Thermoelectric Devices with Surface-Disordered Nanowires

We reviewed some recent ideas to improve the efficiency and power output of thermoelectric nano-devices. We focused on two essentially independent aspects: (i) increasing the charge current by taking advantage of an interplay between the material and the thermodynamic parameters, which is only available in the non-linear regime; and (ii) decreasing the heat current by using nanowires with surface disorder, which helps excite localized phonons at random positions that can strongly scatter the propagating phonons carrying the thermal current.

Copper and Nickel Microsensors Produced by Selective Laser Reductive Sintering for Non-Enzymatic Glucose Detection

In this work, the method of selective laser reductive sintering was used to fabricate the sensor-active copper and nickel microstructures on the surface of glass-ceramics suitable for non-enzymatic detection of glucose. The calculated sensitivities for these microsensors are 1110 and 2080 μA mM−1·cm−2 for copper and nickel, respectively. Linear regime of enzymeless glucose sensing is provided between 0.003 and 3 mM for copper and between 0.01 and 3 mM for nickel. Limits of glucose detection for these manufactured micropatterns are equal to 0.91 and 2.1 µM for copper and nickel, respectively. In addition, the fabricated materials demonstrate rather good selectivity, long-term stability and reproducibility.

Direct validation of dune instability theory

Modern dune fields are valuable sources of information for the large-scale analysis of terrestrial and planetary environments and atmospheres, but their study relies on understanding the small-scale dynamics that constantly generate new dunes and reshape older ones. Here, we designed a landscape-scale experiment at the edge of the Gobi desert, China, to quantify the development of incipient dunes under the natural action of winds. High-resolution topographic data documenting 42 mo of bedform dynamics are examined to provide a spectral analysis of dune pattern formation. We identified two successive phases in the process of dune growth, from the initial flat sand bed to a meter-high periodic pattern. We focus on the initial phase, when the linear regime of dune instability applies, and measure the growth rate of dunes of different wavelengths. We identify the existence of a maximum growth rate, which readily explains the mechanism by which dunes select their size, leading to the prevalence of a 15-m wavelength pattern. We quantitatively compare our experimental results with the prediction of the dune instability theory using transport and flow parameters independently measured in the field. The remarkable agreement between theory and observations demonstrates that the linear regime of dune growth is permanently expressed on low-amplitude bed topography, before larger regular patterns and slip faces eventually emerge. Our experiment underpins existing theoretical models for the early development of eolian dunes, which can now be used to provide reliable insights into atmospheric and surface processes on Earth and other planetary bodies.