Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ ^d . In particular, we show that a family of n≥2d disjoint unit balls in ℝ ^d has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ ^d admits a line transversal if any subfamily of size 4d−1 admits a transversal. Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR).     

Linear and non-linear conduction regimes in broken down gate oxides

We have investigated conduction properties of gate oxides in metal-oxide–semiconductor structures in which dielectric breakdown has occurred. The measurements were performed on p- and n-type substrate samples with oxide thickness ranging from 2.0 to 13.5 nm. It is shown that the post-breakdown differential conductance has two typical modes, which, in terms of the physics of mesoscopic conducting systems, are referred to as linear and non-linear conduction regimes. In this work, we propose an analytic model for the conductance based on the electron transmission properties of quantum point contacts, which captures the essential features and consistently explains both breakdown modes.     

Two phase algorithms for the bi-objective assignment problem

In this paper, we present several algorithms for the bi-objective assignment problem. The algorithms are based on the two phase method, which is a general technique to solve multi-objective combinatorial optimisation (MOCO) problems.     

Route to chaos in the rising dynamics of a bubble chain in a polymeric fluid

We investigate the chaotic dynamics of a bubble chain rising in a polymeric fluid by the experimental temporary measurements, cognitive modelling and analytical analysis. The competition between the stress creation and the relaxation displays complex dynamical features and leads to chaos through a sequence of period doubling bifurcations.     

Quasilinear elliptic system with coupling on nonhomogeneous critical term

We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous. The solutions are obtained from a version of the Symmetric Mountain Pass Theorem. A version of the Concentration-Compactness Principle for this class of systems allows us to verify that the Palais–Smale condition is satisfied below a certain level.     

Highly enantioselective fluoromalonate addition to α,β-unsaturated aldehydes

A highly enantioselective organocatalytic fluoromalonate addition to α,β-unsaturated aldehydes is reported. The reaction is catalyzed by simple and commercially available secondary amines, affording the corresponding 1,4-adducts with high yields and enantioselectivities.     

High Entropy Alloys as Filler Metals for Joining

In the search for applications for alloys developed under the philosophy of the High Entropy Alloy (HEA)-type materials, the focus may be placed on applications where current alloys also use multiple components, albeit at lower levels than those found in HEAs. One such area, where alloys with complex compositions are already found, is in filler metals used for joining. In soldering (<450 °C) and brazing (>450 °C), filler metal alloys are taken above their liquidus temperature and used to form a metallic bond between two components, which remain both unmelted and largely unchanged throughout the process. These joining methods are widely used in applications from electronics to aerospace and energy, and filler metals are highly diverse, to allow compatibility with a broad range of base materials (including the capability to join ceramics to metals) and a large range of processing temperatures. Here, we review recent developments in filler metals relevant to High Entropy materials, and argue that such alloys merit further exploration to help overcome a number of current challenges that need to be solved for filler metal-based joining methods.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).