A Theory of the Casimir Effect for Compact Regions

We develop a mathematically precise framework for the Casimir effect. Our working hypothesis, verified in the case of parallel plates, is that only the regularization-independent Ramanujan sum of a given asymptotic series contributes to the Casimir pressure. As an illustration, we treat two cases: parallel plates, identifying a previous cutoff free version (by G. Scharf and W. W.) as a special case, and the sphere.We finally discuss the open problem of the Casimir force for the cube. We propose an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive sign of the force.Comment: version published, 23 page

Minimal Equation Sets for Output Computation in Object-Oriented Models

Object-oriented models of complex physical systems can have a very large number of equations and variables. For some applications, only a few output variables of the model are of actual interest. This paper presents an application of the well-known Tarjan’s algorithm, that allows to automatically select the minimal set of equations and variables required to compute the time histories of selected outputs of a given model. The application of the algorithm to a simple test case is illustrated in the paper

Second-order quantum nonlinear optical processes in single graphene nanostructures and arrays

Intense efforts have been made in recent years to realize nonlinear optical interactions at the single-photon level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other quantum emitters while the possibility of achieving strong second-order nonlinearities remains unexplored. Here, we describe a novel technique to realize such nonlinearities using graphene, exploiting the strong per-photon fields associated with tightly confined graphene plasmons in combination with spatially nonlocal nonlinear optical interactions. We show that in properly designed graphene nanostructures, these conditions enable extremely strong internal down-conversion between a single quantized plasmon and an entangled plasmon pair, or the reverse process of second harmonic generation. A separate issue is how such strong internal nonlinearities can be observed, given the nominally weak coupling between these plasmon resonances and free-space radiative fields. On one hand, by using the collective coupling to radiation of nanostructure arrays, we show that the internal nonlinearities can manifest themselves as efficient frequency conversion of radiative fields at extremely low input powers. On the other hand, the development of techniques to efficiently couple to single nanostructures would allow these nonlinear processes to occur at the level of single input photons.Comment: 25 pages, 6 figure

Ultrafast Optical Control of the Electronic Properties of ZrTe5ZrTe_5

We report on the temperature dependence of the $ZrTe_5$ electronic properties, studied at equilibrium and out of equilibrium, by means of time and angle resolved photoelectron spectroscopy. Our results unveil the dependence of the electronic band structure across the Fermi energy on the sample temperature. This finding is regarded as the dominant mechanism responsible for the anomalous resistivity observed at T* $\sim$ 160 K along with the change of the charge carrier character from holelike to electronlike. Having addressed these long-lasting questions, we prove the possibility to control, at the ultrashort time scale, both the binding energy and the quasiparticle lifetime of the valence band. These experimental evidences pave the way for optically controlling the thermoelectric and magnetoelectric transport properties of $ZrTe_5$

Primordial Black Holes as Near Infrared Background sources

The near infrared background (NIRB) is the collective light from unresolved sources observed in the band 1-10 $\mu$m. The measured NIRB angular power spectrum on angular scales $\theta \gtrsim 1$ arcmin exceeds by roughly two order of magnitudes predictions from known galaxy populations. The nature of the sources producing these fluctuations is still unknown. Here we test primordial black holes (PBHs) as sources of the NIRB excess. Considering PBHs as a cold dark matter (DM) component, we model the emission of gas accreting onto PBHs in a cosmological framework. We account for both accretion in the intergalactic medium (IGM) and in DM haloes. We self consistently derive the IGM temperature evolution, considering ionization and heating due to X-ray emission from PBHs. Besides $\Lambda$CDM, we consider a model that accounts for the modification of the linear matter power spectrum due to the presence of PBHs; we also explore two PBH mass distributions, i.e. a $\delta$-function and a lognormal distribution. For each model, we compute the mean intensity and the angular power spectrum of the NIRB produced by PBHs with mass 1-$10^3~\mathrm{M}_{\odot}$. In the limiting case in which the entirety of DM is made of PBHs, the PBH emission contributes $<1$ per cent to the observed NIRB fluctuations. This value decreases to $<0.1$ per cent if current constraints on the abundance of PBHs are taken into account. We conclude that PBHs are ruled out as substantial contributors to the NIRB.Comment: Accepted for publication in MNRA

A Damage Detection Approach for Axially Loaded Beam-like Structures Based on Gaussian Mixture Model

Axially loaded beam-like structures represent a challenging case study for unsupervised learning vibration-based damage detection. Under real environmental and operational conditions, changes in axial load cause changes in the characteristics of the dynamic response that are significantly greater than those due to damage at an early stage. In previous works, the authors proposed the adoption of a multivariate damage feature composed of eigenfrequencies of multiple vibration modes. Successful results were obtained by framing the problem of damage detection as that of unsupervised outlier detection, adopting the well-known Mahalanobis squared distance (MSD) to define an effective damage index. Starting from these promising results, a novel approach based on unsupervised learning data clustering is proposed in this work, which increases the sensitivity to damage and significantly reduces the uncertainty associated with the results, allowing for earlier damage detection. The novel approach, which is based on Gaussian mixture model, is compared with the benchmark one based on the MSD, under the effects of an uncontrolled environment and, most importantly, in the presence of real damage due to corrosion

Reduced Basis Method for Parametrized Elliptic Optimal Control Problems

We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique. Copyright \ua9 by SIAM. Unauthorized reproduction of this article is prohibited

Casimir force on a piston

We consider a massless scalar field obeying Dirichlet boundary conditions on the walls of a two-dimensional L x b rectangular box, divided by a movable partition (piston) into two compartments of dimensions a x b and (L-a) x b. We compute the Casimir force on the piston in the limit L -> infinity. Regardless of the value of a/b, the piston is attracted to the nearest end of the box. Asymptotic expressions for the Casimir force on the piston are derived for a << b and a >> b.Comment: 10 pages, 1 figure. Final version, accepted for publication in Phys. Rev.

Voluntary nicotine consumption triggers in vivo potentiation of cortical excitatory drives to midbrain dopaminergic neurons

International audienceActive response to either natural or pharmacological reward causes synaptic modifications to excitatory synapses on dopamine (DA) neurons of the ventral tegmental area (VTA). Here, we examine these modifications using nicotine, the main addictive component of tobacco, which is a potent regulator of VTA DA neurons. Using an in vivo electrophysiological technique, we investigated the role of key components of the limbic circuit, the infralimbic cortex (ILCx) and the bed nucleus of the stria terminalis (BNST), in operant behaviors related to nicotine reward. Our results indicated that nicotine self-administration in rats, but not passive delivery, triggers hyperactivity of VTA DA neurons. The data suggest that potentiation of the ILCx-BNST excitatory pathway is involved in these modifications in VTA DA neurons. Thus, recruitment of these specific excitatory inputs to VTA DA neurons may be a neural correlate for the learned association between active responding and the reward experience