The Localization Length of Stationary States in the Nonlinear Schreodinger Equation

For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the ``white noise'' random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust

Non-minimal monopoles of the Dirac type as realization of the censorship conjecture

We discuss a class of exact solutions of a three-parameter non-minimally extended Einstein-Maxwell model, which are attributed to non-minimal magnetic monopoles of the Dirac type. We focus on the investigation of the gravitational field of Dirac monopoles for those models, for which the singularity at the central point is hidden inside of an event horizon independently on the mass and charge of the object. We obtained the relationships between the non-minimal coupling constants, for which this requirement is satisfied. As explicit examples, we consider in detail two one-parameter models: first, non-minimally extended Reissner-Nordstr\"om model (for the magnetically charged monopole), second, the Drummond-Hathrell model.Comment: 9 pages; one reference added, accepted to Phys. Rev.

Correlation Between Structure And C-Afm Contrast Of 180-Degree Domain Walls In Rhombohedral Bati03

Using Landau-Ginzburg-Devonshire theory we describe 180-degree domain wall structure, intrinsic energy and carrier accumulation in rhombohedral phase of BaTiO3 as a function of the wall orientation and flexoelectric coupling strength. Two types of domain wall structures (phases of the wall) exist depending on the wall orientation. The low-energy 'achiral' phase occurs in the vicinity of the {110} wall orientation and has odd polarization profile invariant with respect to inversion about the wall center. The second 'chiral' phase occurs around {211} wall orientations and corresponds to mixed parity domain walls that may be of left-handed or right-handed chirality. The transformation between the phases is abrupt, accompanied with 20-30% change of the domain wall thickness and can happen at fixed wall orientation with temperature change. We suggest that the phase transition may be detected through domain wall thickness change or by c-AFM. The structure of the domain wall is correlated to its conductivity through polarization component normal to the domain wall, which causes free carriers accumulation. Depending on the temperature and flexoelectric coupling strength relative conductivity of the wall becomes at least one order of magnitude higher than in the single-domain region, creating c-AFM contrast enhancement pronounced and detectable.Comment: 31 pages, 10 figures, Supplementary material

Probing the Influence of Single-Site Mutations in the Central Cross-β Region of Amyloid β (1–40) Peptides

Amyloid β (Aβ) is a peptide known to form amyloid fibrils in the brain of patients suffering from Alzheimer’s disease. A complete mechanistic understanding how Aβ peptides form neurotoxic assemblies and how they kill neurons has not yet been achieved. Previous analysis of various Aβ40 mutants could reveal the significant importance of the hydrophobic contact between the residues Phe19 and Leu34 for cell toxicity. For some mutations at Phe19, toxicity was completely abolished. In the current study, we assessed if perturbations introduced by mutations in the direct proximity of the Phe19/Leu34 contact would have similar relevance for the fibrillation kinetics, structure, dynamics and toxicity of the Aβ assemblies. To this end, we rationally modified positions Phe20 or Gly33. A small library of Aβ40 peptides with Phe20 mutated to Lys, Tyr or the non-proteinogenic cyclohexylalanine (Cha) or Gly33 mutated to Ala was synthesized. We used electron microscopy, circular dichroism, X-ray diffraction, solid-state NMR spectroscopy, ThT fluorescence and MTT cell toxicity assays to comprehensively investigate the physicochemical properties of the Aβ fibrils formed by the modified peptides as well as toxicity to a neuronal cell line. Single mutations of either Phe20 or Gly33 led to relatively drastic alterations in the Aβ fibrillation kinetics but left the global, as well as the local structure, of the fibrils largely unchanged. Furthermore, the introduced perturbations caused a severe decrease or loss of cell toxicity compared to wildtype Aβ40. We suggest that perturbations at position Phe20 and Gly33 affect the fibrillation pathway of Aβ40 and, thereby, influence the especially toxic oligomeric species manifesting so that the region around the Phe19/Leu34 hydrophobic contact provides a promising site for the design of small molecules interfering with the Aβ fibrillation pathway

Ball on a beam: stabilization under saturated input control with large basin of attraction

This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan form of its model, linearized near the unstable equilibrium. The limits on the voltage, fed to the motor, are taken into account explicitly. The straight beam-and-ball system has one unstable mode in the motion near the equilibrium point. The proposed control law ensures that the basin of attraction coincides with the controllability domain. The circular beam-and-ball system has two unstable modes near the equilibrium point. Therefore, this device, never considered in the past, is much more difficult to control than the straight beam-and-ball system. The main contribution is to propose a simple new control law, which ensures by adjusting its gain parameters that the basin of attraction arbitrarily can approach the controllability domain for the linear case. For both nonlinear systems, simulation results are presented to illustrate the efficiency of the designed nonlinear control laws and to determine the basin of attraction

The squeezable nanojunction as a tunable light-matter interface for studying photoluminescence of 2D materials

We study photoluminescence (PL) of MoS2 monolayers in optical cavities that can be tuned in operando. Technically, we use the recently developed squeezable nanojunction (SNJ). It is a versatile mechanical setup that has been useful to study thermoelectric effects at electronic tunneling distances. Here, we emphasize on a cavity with 0–3 micrometer distance with optical access. Due to the tunable cavity, we see strong distortions of PL spectra. By an analysis of the ensemble, we identify a normalization protocol that gives access to disentangling the contributions from excitation, gating and emission. The systematic evolution of data reconfirms the drastic influence of the local electromagnetic mode budget on the spectral properties. The experiment further underscores the broadband application range of the SNJ technique, able for combining (nano-) electronic functionality with optical access and a tunable light-matter interface

Own-company stockholding and work effort preferences of an unconstrained executive

We develop a framework for analyzing an executive's own-company stockholding and work effort preferences. The executive, characterized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive's utility-maximizing personal investment and work effort strategy is derived in closed form, and a utility indifference rationale is applied to determine his required compensation. Being unconstrained byperformance contracting, the executive's work effort strategy establishes a base case for theoretical or empirical assessment of the benefits or otherwise of constraining executives with performance contracting

Search for squarks and gluinos in events with isolated leptons, jets and missing transverse momentum at s√=8 TeV with the ATLAS detector

The results of a search for supersymmetry in final states containing at least one isolated lepton (electron or muon), jets and large missing transverse momentum with the ATLAS detector at the Large Hadron Collider are reported. The search is based on proton-proton collision data at a centre-of-mass energy s√=8 TeV collected in 2012, corresponding to an integrated luminosity of 20 fb−1. No significant excess above the Standard Model expectation is observed. Limits are set on supersymmetric particle masses for various supersymmetric models. Depending on the model, the search excludes gluino masses up to 1.32 TeV and squark masses up to 840 GeV. Limits are also set on the parameters of a minimal universal extra dimension model, excluding a compactification radius of 1/R c = 950 GeV for a cut-off scale times radius (ΛR c) of approximately 30

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal