Line tension and nanometer drop wettability on solid surfaces

The dimensional dependence of the angle of solid surface wetting by a small drop on the latter’s size R and radius of the wetting outline r is considered. Numerical values of specific linear energy γ?(r) and line tension σ _r (r) of the wetting outline are calculated for a nanometer tin drop-substrate surface-aluminum film system. It is shown that wetting angle θ(R,r) in the drop-substrate surface system increases as the wetting outline’s radius decreases.     

Joint densities for random walks in the plane

We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for p_n(r, θ) is developed for this purpose which does not require radial symmetry, but does require that p_n(r, θ) = 0 when r exceeds some maximum radius, R.     

The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.     

First-order aberration of a misfocused self-imaging system

We analyze the characteristics of a self-imaging system that appear across a misfocused image plane. We approach this problem from the point of view of aberration theory. First, we derive the aberration functions (corresponding to several self-imaging rays of different orders) which are linear in a small shift of focus, and then we examine their roles in the amplitude spectra of misfocused self-images. We show that the aberration of the mth-order self-imaging ray is responsible for a lateral shift of the image amplitude component of frequency m/Mp, where M is the magnification of the system and p is the fundamental period of an object grating. We also analyze the role of wavefront aberrations in the image irradiance as an observable quantity. We then show that the theoretical estimation of irradiance of the aberrated image is in good agreement with the experiment and the focus-shift aberration can exert a severe effect on the irradiance spectrum of image in a complicated way.     

The Green's function of confined electrons in an external magnetic field: Analytical formulation

We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r and R (quantum ring).     

Short-time dynamics of Fe2/V13 magnetic superlattice models

Critical relaxation from a low-temperature fully ordered state of Fe₂/V₁₃ iron-vanadium magnetic superlattice models has been studied using the method of short-time dynamics. Systems with three variants of the ratio R of inter-to intralayer exchange coupling have been considered. Particles with N = 262144 spins have been simulated with periodic boundary conditions. Calculations have been performed using the standard Metropolis algorithm of the Monte Carlo method. The static critical exponents of magnetization and correlation radius, as well as the dynamic critical exponent, have been calculated for three R values. It is established that a small decrease in the exchange ratio (from R = 1.0 to 0.8) does not significantly influence the character of the short-time dynamics in the models studied. A further significant decrease in this ratio (to R = 0.01), for which a transition from three-dimensional to quasi-two-dimensional magnetism is possible, leads to significant changes in the dynamic behavior of iron-vanadium magnetic superlattice models.     

Numerical simulation of magnetic fluid hyperthermia based on multiphysics coupling and recommendation on preferable treatment conditions

In this study, we established a multiphysics coupling model of magnetic fluid hyperthermia (MFH), using complex magnetic permeability to solve the magnetic losses of magnetic nanoparticles (MNPs). The experiments were performed to verify the validity of numerical coupling method. The optimal treatment time (OTT) was regarded as the time required for the lowest temperature point of the tumor to attain the damage criteria. The OTT increased by about 42 s as the tumor radius increased by 1 cm, and decreased by 10 s for the increase in MNP dose per gram of tumor by 1 mg. To achieve cost-effective therapies under moderate treatment conditions, the preferable ranges of external magnetic field intensity H₀ and frequency f, MNP radius R and volume fraction $?$ are 3–11 kA/m, 200–500 kHz, 8–10 nm, and 5%–10%, respectively. It is greatly encouraged to adopt the combination of higher H₀ (8–11 kA/m) and lower f (200–300 kHz), and the conjunction of higher R and $?$. There was a slight thermal damage to normal tissues due to eddy current loss. In conclusion, MFH can provide an excellent therapeutic effect for deep tumors.     

The scattering of strings by a black hole

We study the elastic and inelastic scattering of strings by a Schwarzschild's black hole. Pair creation takes place (and in all the modes) as a consequence of the composite structure (oscillator modes) of the string. The S-matrix amplitudes including the pair-creation rate are found at first order in √α'/R_S (√α' = Planck's length and R_S = Schwarzschild's radius). Explicit computations are made in the weak-field expansion in powers of (R_S/b)^D−3 (b = impact parameter of the string center of mass). The deflection angle and cross sections are found. The quantum string corrections to the gravitational analogue of Rutherford's scattering are computed (these are of order α'²). The pair-creation or radiation amplitude we find here is of order α', it is non-thermal and of different origin than Hawking radiation.     

On the defective NR-PC flat lens for lightwave target detection and imaging

Influence of the defective cylinder air holes of negative-refraction photonic crystal (NR-PC) lens on the performance of lightwave target detection and imaging are studied with finite-difference time-domain method in the paper. Numerical simulations indicate that significant enhancement of the scattering signal can be obtained using the NR-PC flat lens; consequently, great improvement of the refocusing gain as well as the imaging resolution will be provided. We further study the effect on target detection and imaging using the defective NR-PC flat lens. Using dynamic scanning scheme, it is found that its focusing resolution is better than the non-defective lens. We can also get better resolution by appropriately decreasing the radius of the defective cylinder (R = 0.3a). In conclusion, appropriate radius of the defective cylinder (R = 0.3a) will provide better image resolution.     

Resonant scattering of light in a near-black-hole metric

We show that low-energy photon scattering from a body with radius R slightly larger than its Schwarzschild radius r _s resembles black-hole absorption. This absorption occurs via capture resulting in one of the many long-lived, densely packed resonances that populate the continuum. The lifetimes and density of these meta-stable states tend to infinity in the limit r _s →R. We determine the energy-averaged cross section for particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus a non-singular static metric may trap photons for arbitrarily long times, making it appear completely ‘black’ before the actual formation of a black hole.     

Optimum correction conditions for aberration-corrected HRTEM SiC dumbbells chemical imaging

Over the last decade, the spatial resolution of transmission electron microscopes has been considerably improved thanks to the development of aberration correctors. At the same time, image interpretation has become easier as the influence of instrument aberrations on image intensity has been reduced for phase contrast imaging. New aberration-corrected microscopes now offer the possibility to extract both the structural and the chemical information from a quantitative analysis of the image's contrast, which is promising in many fields of materials science where knowledge of the chemical content at the atomic scale is crucial. However, appropriate imaging conditions must be used for a quantitative analysis of the image at the sub-angström scale. In this paper, we focus on the impact of chromatic and geometric aberrations on phase contrast and we compare the advantages offered by the few optimum imaging conditions proposed in the literature. Effects of residual aberrations are also considered while the influence of chromatic aberration correction in future C_s/C_c-corrected instruments is emphasized. A critical value of C_c is given depending on the instrumental parameters. Silicon carbide imaging using a C_s-corrected microscope is presented and illustrates the assessments derived from the theoretical study of residual aberration influence on phase contrast imaging.     

Three-dimensional Wigner molecules formed from an assembly of confined but Coulombically repelling electrons

We first consider N Coulombically interacting electrons confined within a sphere of radius R by an infinite potential barrier. Scaling properties of the Hamiltonian are first discussed, followed by the virial theorem. In the limit of large R and N, it is shown that the problem can be reduced to the solution of N point charges −|e| constrained to move on the surface of a sphere of radius R_W here defined as Wigner radius. Finally, the results of the above model are compared with those of harmonically confined electrons.     

Conditions for identical position of optimal image plane for axial imaging with different values of f-number

By analysis of the dependence of longitudinal spherical aberration on the numerical aperture, it is possible to find such values of the numerical aperture, where spherical aberration is zero. Such values of the numerical aperture are called correction zones. The work theoretically analyses the described problem and equations are given for wave aberration coefficients using correction zones for spherical aberration of the third and the fifth order. Our work presents an analysis of optimal values of correction zones and an optimal position of the center of the reference sphere based on the variance of wave aberration for the image quality evaluation. Relations are described for calculation of correction zones of an optical system having an identical position of the optimal image plane for two values of the f-number. The analysis of optical systems using correction zones is performed on an example.     

Determination of the root-mean-square radius of the deuteron from present-day experimental data on neutron-proton scattering

The correlation between the root-mean-square matter radius of the deuteron, r _m , and its effective radius, ρ, is investigated. A parabolic relationship between these two quantities makes it possible to determine the root-mean-square radius r _m to within 0.01% if the effective radius ρ is known. The matter (r _m ), structural (r _d ), and charge (r _ch) radii of the deuteron are found with the aid of modern experimental results for phase shifts from the SAID nucleon-nucleon database, and their values are fully consistent with their counterparts deduced by using the experimental value of the effective deuteron radius due to Borbély and his coauthors. The charge-radius value of 2.124(6) fm, which was obtained with the aid of the SAID nucleon-nucleon database, and the charge-radius value of 2.126(12) fm, which was obtained with the aid of the experimental value of the effective radius ρ, are in very good agreement with the present-day chargeradius value of 2.128(11) fm, which was deduced by Sick and Trautmann by processing world-average experimental data on elastic electron scattering by deuterons with allowance for Coulomb distortions.     

Multiple color-image fusion and watermarking based on optical interference and wavelet transform

A novel multiple color-image fusion and watermarking using optical interference and wavelet transform is proposed. In this method, each secret color image is encoded into three phase-only masks (POMs). One POM is constructed as user identity key and the other two POMs are generated as user identity key modulated by corresponding secret color image in gyrator transform domain without using any time-consuming iterative computations or post-processing of the POMs to remove inherent silhouette problem. The R, G, and B channels of different user identity keys POM are then individually multiplied to get three multiplex POMs, which are exploited as encrypted images. Similarly the R, G, and B channels of other two POMs are independently multiplied to obtain two sets of three multiplex POMs. The encrypted images are fused with gray-level cover image to produce the final encrypted image as watermarked image. The secret color images are shielded by encrypted images (which have no information about secret images) as well as cover image (which reveals no information about encrypted images). These two remarkable features of the proposed system drastically reduce the probability of the encrypted images to be searched and attacked. Each individual user has an identity key and two phase-only keys as three decryption keys besides transformation angles regarded as additional keys. Theoretical analysis and numerical simulation results validate the feasibility of the proposed method.     

Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints

A number of methods using temporal and spatial constraints have been proposed for reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. The complex data can be constrained or regularized in a number of different ways, for example, the time derivative of the magnitude and phase image voxels can be constrained separately or jointly. Intuitively, the performance of different regularizations will depend on both the data and the chosen temporal constraints. Here, a complex temporal total variation (TV) constraint was compared to the use of separate real and imaginary constraints, and to a magnitude constraint alone. Projection onto Convex Sets (POCS) with a gradient descent method was used to implement the diverse temporal constraints in reconstructions of DCE MRI data. For breast DCE data, serial POCS with separate real and imaginary TV constraints was found to give relatively poor results while serial/parallel POCS with a complex temporal TV constraint and serial POCS with a magnitude-only temporal TV constraint performed well with an acceleration factor as large as R=6. In the tumor area, the best method was found to be parallel POCS with complex temporal TV constraint. This method resulted in estimates for the pharmacokinetic parameters that were linearly correlated to those estimated from the fully-sampled data, with K^trans,R=6=0.97 K^trans,R=1+0.00 with correlation coefficient r=0.98, k_ep,R=6=0.95 k_ep,R=1+0.00 (r=0.85). These results suggest that it is possible to acquire highly undersampled breast DCE-MRI data with improved spatial and/or temporal resolution with minimal loss of image quality.