Squark Pair Production at Muon Colliders in the MSSM with CP Violation

We study the pair production of scalar quark in a muon collider within the MSSM with CP violation. We show that including the CP phases can strongly affect the cross section of the process: \(\mu^{+}\mu^{-}\rightarrow \tilde{q}_{i}\bar{\tilde{q}}_{j}\). This could have an important impact on the search for squarks and the determination of the MSSM parameters at future colliders.     

Fast free-surface detection and level-set function definition in SPH solvers

The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.     

Validity diagrams of statistical energy analysis

This paper is concerned with the validity domain of statistical energy analysis (SEA) which is defined in terms of four criteria. The mode count N and the modal overlap M must be high, the normalized attenuation factor and the coupling strength γ must be small. The application of dimensional analysis on the governing equations of plates gives the space of dimensionless parameters in which the validity domain of SEA must be delimited. This domain is discussed on the basis of geometry of the surfaces delimiting it. The diagrams of validity of SEA are introduced and discussed. A numerical simulation on a couple of rectangular plates coupled along one edge illustrates the theoretical approach.     

Ostwald ripening in nanoalloys: when thermodynamics drives a size-dependent particle composition

Ostwald ripening has been broadly studied because it plays a determinant role in the evolution of cluster size during both chemical and physical synthesis of nanoparticles. This thermoactivated process causes large particles to grow, drawing material from the smaller particles, which shrink. However, this phenomenon becomes more complex when considering the coarsening of metallic alloy clusters. The present experimental and theoretical investigations show that the relative composition of CoPt nanoparticles can be strongly modified during high temperature annealing and displays a size-dependent behavior. This compositional change originates from the higher evaporation rate of Co atoms from the nanoparticles. More importantly, this effect is expected in all alloy clusters containing species with different mobilities.     

On the generalized Fréchet functional equation with constant coefficients and its stability

We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive. We also obtain a theorem on the Ulam type stability of the equation. In its proof we use a fixed point result to show the existence of an exact solution of the equation that is close to a given approximate solution.     

Tangent cones and C1 regularity of definable sets

Let $X?{\mathbb{R}}^n$ be a connected locally closed set which is definable in an o-minimal structure. We prove that the following three statements are equivalent: (i) X is a $C^1$ manifold, (ii) the tangent cone and the paratangent cone of X coincide at every point in X, (iii) for every $x\in X$, the tangent cone of X at the point x is a k-dimensional linear subspace of ${\mathbb{R}}^n$ (k does not depend on x) varies continuously in x, and the density $\theta (X,x)<3/2$.     

Determinacy of refinements to the difference hierarchy of co-analytic sets

In this paper we develop a technique for proving determinacy of classes of the form ${\omega }^2\text{-}{\mathrm{\Pi }}_1^1+\mathrm{\Gamma }$ (a refinement of the difference hierarchy on ${\mathrm{\Pi }}_1^1$ lying between ${\omega }^2\text{-}{\mathrm{\Pi }}_1^1$ and $({\omega }^2+1)\text{-}{\mathrm{\Pi }}_1^1$) from weak principles, establishing upper bounds for the determinacy-strength of the classes ${\omega }^2\text{-}{\mathrm{\Pi }}_1^1+{\mathrm{\Sigma }}_{\alpha }^0$ for all computable α and of ${\omega }^2\text{-}{\mathrm{\Pi }}_1^1+{{\mathrm{\Delta }}^1}_1$. This bridges the gap between previously known hypotheses implying determinacy in this region.     

Explicit formulas for C1,1 and Cconv1,ω extensions of 1-jets in Hilbert and superreflexive spaces

Given X a Hilbert space, ω a modulus of continuity, E an arbitrary subset of X, and functions $f:E\to \mathbb{R}$, $G:E\to X$, we provide necessary and sufficient conditions for the jet $(f,G)$ to admit an extension $(F,\mathrm{?}F)$ with $F:X\to \mathbb{R}$ convex and of class $C^{1,\omega }(X)$, by means of a simple explicit formula. As a consequence of this result, if ω is linear, we show that a variant of this formula provides explicit $C^{1,1}$ extensions of general (not necessarily convex) 1-jets satisfying the usual Whitney extension condition, with best possible Lipschitz constants of the gradients of the extensions. Finally, if X is a superreflexive Banach space, we establish similar results for the classes $C_{\mathrm{conv}}^{1,\alpha }(X)$.     

Robust optimization of noisy blackbox problems using the Mesh Adaptive Direct Search algorithm

Blackbox optimization problems are often contaminated with numerical noise, and direct search methods such as the Mesh Adaptive Direct Search (MADS) algorithm may get stuck at solutions artificially created by the noise. We propose a way to smooth out the objective function of an unconstrained problem using previously evaluated function evaluations, rather than resampling points. The new algorithm, called Robust-MADS is applied to a collection of noisy analytical problems from the literature and on an optimization problem to tune the parameters of a trust-region method.