A mean-field model of Integrate-and-Fire neurons: non-linear stability
of the stationary **solutions**

7/10 relevant

arXiv

Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons

**solution**as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the linear problem using a Lyapunov-Schmidt reduction and provide an expansion of both the nonlinear eigenvalue and the

**solution**. We further prove that if the linear eigenvalue is real and the nonlinear problem $\mathcal P\mathcal T$-symmetric, then the bifurcating nonlinear eigenvalue remains real. These general results are then applied in the context of surface plasmon polaritons (SPPs), i.e. localized

**solutions**for the nonlinear Maxwell's equations in the presence of one or more interfaces between dielectric and metal layers. We obtain the existence of transverse electric SPPs in certain $\mathcal P\mathcal T$-symmetric configurations.

6/10 relevant

arXiv

Noise effects on the stochastic Euler-Poincar'{e} equations

**solution**. Expand abstract.

**solution**to the periodic boundary value problem of the stochastic Euler-Poincar\'{e} equation with nonlinear multiplicative noise. Then we consider the noise effects with respect to the continuity of the

**solution**map and the wave breaking phenomenon. Even though the noise has some already known regularization effects, almost nothing is clear to the problem whether the noise can improve the continuity/stability of the

**solution**map, neither for general SPDEs nor for special examples. As a new setting to analyze initial data dependence, we introduce the concept of the stability of the exiting time (See Definition 1.4 below) and construct an example to show that for the stochastic Euler-Poincar\'{e} equations, the multiplicative noise (It\^{o} sense) cannot improve the stability of the exiting time and improve the continuity of the dependence on initial data simultaneously. Then we consider the noise effect on the wave breaking phenomenon in the particular 1-D case, namely the stochastic Camassa--Holm equation. We show that under certain condition on the initial data, wave breaking happens with positive probability and we provide a lower bound of such probability. We also characterize the breaking rate of breaking

**solution**.

5/10 relevant

arXiv

Geometrical aspects of ads/cft

**solution**. Furthermore, we prove a non-existence theorem for AdS$_3$

**solutions**preserving more than 16 supersymmetries. Finally, we demonstrate that warped Minkowski space backgrounds of the form $\mathbb{R}^{n-1,1}\times_w M^{D-n}$ ($n\geq 3,D=10,11$) in 11-dimensional and type II supergravities preserving strictly more than 16 supersymmetries and with fields, which may not be smooth everywhere, are locally isometric to the Minkowski vacuum $\mathbb{R}^{D-1,1}$. In particular, all such flux compactification vacua of these theories have the same local geometry as the maximally supersymmetric vacuum $\mathbb{R}^{n-1,1}\times T^{d-n}$.

4/10 relevant

arXiv

Dirac Particle with Memory: Proper Time Non-Locality

**solutions**is described. Expand abstract.

**solution**are suggested. The asymptotic behavior of the proposed

**solutions**is described.

4/10 relevant

arXiv

Continuity of **solutions** for the phi-Laplacian operator

**solutions**for the so called {\em $\phi-$Laplacian} $\Delta_\phi$ with respect to domain perturbations. We point out that this kind of results can be extended to a more general class of operators including, for instance, nonlocal nonstandard growth type operators.

5/10 relevant

arXiv

The Effect of Vanadate, Phosphate, Fluoride Compounds and Their Effect on the Aqueous Corrosion of Magnesium Alloy AZ31 in Dilute Chloride **Solutions**

**solutions**with millimolar additions of NaVO3, Na3PO4, Na2HPO4, NaF and various pairings to assess their ability to inhibit corrosion kinetics and retard localized corrosion. Expand abstract.

**solutions**with millimolar additions of NaVO3, Na3PO4, Na2HPO4, NaF and various pairings to assess their ability to inhibit corrosion kinetics and retard localized corrosion. Each of the candidate inhibitors reduced the corrosion rate of the alloy to some degree. A Na3PO4 - NaVO3 pair produced a powerful inhibiting response decreasing the corrosion rate to about 10-7 A/cm2, which was two orders of magnitude lower than the uninhibited control case. A Bliss Independence assessment indicated that this inhibitor pair acted synergistically. A Na2HPO4 - NaVO3 pair reduced the corrosion rate to 10-6 A/cm2 but was not assessed to be acting synergistically. The NaVO3 - NaF pair did not reduce the corrosion rate significantly compared to the control case and was an antagonistic pairing. SEM imaging showed film formation due to exposure, which appears to be the origins of the observed inhibition. The resistance to localized corrosion was assessed as the difference in the breakdown potential and the corrosion potential with larger values indicating a lower probability of localized corrosion during free corrosion exposures. Effects of the inhibitors on this characteristic were mixed, but each of the inhibitor pairs yielded potential differences in excess of 100mV. A conceptual conversion coating process based on a mixture of vanadate and phosphate compounds were demonstrated. A fluoride-bearing formulation produced coatings whose total impedance was increased by a factor or 2 compared to an uncoated control. A fluoride-free formulation produced coatings whose corrosion resistance was increased by more than a factor of 3.

5/10 relevant

Preprints.org

Data Processing and Information Classification: An In-Memory Approach

**solution**is the Processing-In-Memory (PIM) approach. Expand abstract.

**solution**commonly adopted is to send these data to server farms to be remotely elaborated. The drawback is a huge battery drain due to high amount of information that must be exchanged. To compensate this problem data must be processed locally, near the sensor itself. But this

**solution**requires huge computational capabilities. While microprocessors, even mobile ones, nowadays have enough computational power, their performance are severely limited by the Memory Wall problem. Memories are too slow, so microprocessors cannot fetch enough data from them, greatly limiting their performance. A

**solution**is the Processing-In-Memory (PIM) approach. New memories are designed that are able to elaborate data inside them eliminating the Memory Wall problem. In this work we present an example of such system, using as a case of study the Bitmap Indexing algorithm. Such algorithm is used to classify data coming from many sources in parallel. We propose an hardware accelerator designed around the Processing-In-Memory approach, that is capable of implementing this algorithm and that can also be reconfigured to do other tasks or to work as standard memory. The architecture has been synthesized using CMOS technology. The results that we have obtained highlights that, not only it is possible to process and classify huge amount of data locally, but also that it is possible to obtain this result with a very low power consumption.

5/10 relevant

Preprints.org

Bootstraps to Strings: Solving Random Matrix Models with Positivity

**solution**. This approach is tested on single and multi-matrix models and handily reproduces known

**solutions**. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

5/10 relevant

arXiv

Evaporation Induced Rayleigh-Taylor Instabilities in Polymer **Solutions**

**solutions**is crucial in many applications such as the production of film coatings. It is well known that solvent evaporation in polymer

**solutions**can lead to Rayleigh-B\'enard or Marangoni-type instabilities. Here we reveal another mechanism, namely that evaporation can cause the interface to display Rayleigh-Taylor instabilities due to the build-up of a dense layer at the air-liquid interface. We study experimentally the onset time ($t_p$) of the instability as a function of the macroscopic properties of aqueous polymer solutions, which we tune by varying the polymer concentration ($c_0$), molecular weight and polymer type. In dilute solutions, $t_p$ shows two limiting behaviors depending on the polymer diffusivity. For high diffusivity polymers (low molecular weight), the pluming time scales as $c_0^{-2/3}$. This result agrees with previous studies on gravitational instabilities in miscible systems where diffusion stabilizes the system. On the other hand, in low diffusivity polymers the pluming time scales as $c_0^{-1}$. The stabilizing effect of an effective interfacial tension, similar to those in immiscible systems, explains this strong concentration dependence. Above a critical concentration, $\hat{c}$, viscosity delays the growth of the instability, allowing time for diffusion to act as the dominant stabilizing mechanism. This results in $t_p$ scaling as $(\nu/c_0)^{2/3}$.

6/10 relevant

arXiv