Relaxation of Paramagnetic Centers during Modulation of a Stationary Magnetic Field

It has been found that the phase shift _min in the synchronous detection block that ensures the minimum amplitude of the EPR lines of ruby, diphenylpicrylhydrazyl, and MnSO₄·5H₂O, depends on the amplitude of the modulationH _m of a stationary magnetic field. The dependence of _min on H _m is explained by the inertial nature of the recovery of the stationary states of paramagnetic centers on a change in the magnetic field strength.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δ _h (γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ | representation we find that Δ _h (γ,ε;κ) is just a pure squeezed coherent state density operator | γ,ε〉 _{κ κ} 〈γ,ε |, which brings much convenience for studying Husimi distribution, so we name Δ _h (γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution. Work supported by the National Natural Science Foundation under the grant: 10775097.     

Crime and punishment: Does it pay to punish?

Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension.     

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.     

Obtaining certificates for complete synchronisation of coupled oscillators

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators.     

Scanning tunneling microscopy/spectroscopy on Au nanoparticles assembled using lauryl amine (LAM) and octadecane thiol (ODT)

In this report, we demonstrate scanning tunneling microscopy and spectroscopy on thin films of lauryl amine (LAM) and octadecane thiol (ODT) protected gold nanoparticles. We show that the zero current in the I-V curves (measure of Coulomb blockade (CB) of the nanoparticles) depends on the properties of the spacer molecule. In both the cases the gap voltage and the tunneling current at which the images are obtained are quite different which is further confirmed from the fitting performed based on the orthodox theory. The values for the capacitance and charging energy obtained from the fitting for ODT capped particles are comparable to the values obtained using spherical capacitor model. In contrast, values of these parameters were found to differ for LAM capped nanoparticles. While imaging, ODT capped nanoparticles were observed to drag along the scan direction leading to ordering of particles. Images of LAM capped gold nanoparticles show local ordering in self-assembly of particles although no evidence of large scale ordering in spatial Fourier transform was seen. These observations suggest that nanoparticles with larger CB would be imaged nonevasively in contrast to small CB systems for which tip induced effects will be dominant. In both the systems the current was found to rise faster than theoretical curves based on the orthodox theory suggesting that mechanism of charge transfer in this case may involve field emission rather than tunneling through a rectangular barrier. An attempt has been made to explain charge transfer based on Fowler-Nordheim (F-N) plots of the I-V curves.     

Modulation of the Acher’s limit by medium thickness in [FeCoB/ZnO]50 multilayers

This work investigates the high frequency characteristics of [FeCoB/ZnO]₅₀ multilayers with different ZnO thickness. The results reveal that the Acher’s limit of [FeCoB/ZnO]₅₀ multilayers can be modulated by medium thickness. Increasing medium layer thickness is favorable for breaking through the Acher’s limit. It is found that the differences of Acher’s limit between multilayers and single layers are caused by magnetic interface anisotropy related to interface roughness and some unknown factor.