Scattering in thick multifractal clouds, Part II: Multiple scattering

In Part I of this paper, we developed asymptotic approximations for single photon scattering in thick, highly heterogeneous, “Log-Lévy” multifractal clouds. In Part II, theoretical multiple scattering predictions are numerically tested using Monte Carlo techniques, which show that, due to long range correlations, the photon paths are “subdiffusive” with the corresponding fractal dimensions tending to increase slowly with mean optical thickness. We develop reasonably accurate statistical relations between N scatter statistics in thick clouds and single scatter statistics in thin clouds. This is explored further using discrete angle radiative transfer (DART) approach in which the radiances decouple into non-interacting families with only four (for 2-D clouds) radiance directions each. Sparse matrix techniques allow for rapid and extremely accurate solutions for the transfer; the accuracy is only limited by the spatial discretization.By “renormalizing” the cloud density, we relate the mean transmission statistics to those of an equivalent homogeneous cloud. This simple idea is remarkably effective because two complicating effects act in contrary directions: the “holes” which lead to increased single scatter transmission and the tendency for multiply scattered photons to become “trapped” in optically dense regions, thus decreasing the overall transmission.     

Modeling of exchange bias in the antiferromagnetic (core)/ferromagnetic (shell) nanoparticles with specialized shapes

Zero-field-cooled (ZFC) and field-cooled (FC) hysteresis loops of egg- and ellipsoid-shaped nanoparticles with inverted ferromagnetic (FM)-antiferromagnetic (AFM) core-shell morphologies are simulated using a modified Monte Carlo method, which takes into account both the thermal fluctuations and energy barriers during the rotation of spin. Pronounced exchange bias (EB) fields and reduced coercivities are obtained in the FC hysteresis loops. The analysis of the microscopic spin configurations allows us to conclude that the magnetization reversal occurs by means of the nucleation process during both the ZFC and FC hysteresis branches. The nucleation takes place in the form of “sparks” resulting from the energy competition and the morphology of the nanoparticle. The appearance of EB in the FC hysteresis loops is only dependent on that the movements of “sparks” driven by magnetic field at both branches of hysteresis loops are not along the same axis, which is independent of the strength of AFM anisotropy. The tilt of “spark” movement with respect to the symmetric axis implies the existence of additional unidirectional anisotropy at the AFM/FM interfaces as a consequence of the surplus magnetization in the AFM core, which is the commonly accepted origin of EB. Our simulations allow us to clarify the microscopic mechanisms of the observed EB behavior, not accessible in experiments.     

长程差分吸收光谱技术气体浓度反演误差的定量估计

长程差分吸收光谱法(LP-DOAS)是基于最小二乘原理来反演大气痕量气体浓度的。LP-DOAS能对痕量气体进行高灵敏的测量,但是还没有统计的方法定量确定LP-DOAS反演误差。痕量气体的吸收通常很弱,外来影响因素决定了检测限和测量精度,其被误当做真正的吸收,增加了没有统计特性的噪声到残差中,导致最小二乘拟合误差(err(LSQ))有一个明显的误估计。研究采用蒙特卡罗方法,通过残差的循环移位定量确定差分吸收光谱法反演气体浓度的误差。实验结果表明,蒙特卡罗方法可以定量估计差分吸收光谱法反演误差,误估计因子为1.13,而err(LSQ)为3.12。     

Monte Carlo investigation of the effect of small cutouts on beam profile parameters of 12 and 14 MeV electron beams

Cutouts, which are used as field-shaping shield, affect several electron beam parameters. These effects are more observable for small field sizes and high energy electron beams. Owing to the fact that small fields prevent the lateral scatter equilibrium, at higher energies larger field radius is required for the establishment of lateral equilibrium.The profile curves are derived from circular, triangular, and square cutout shapes and size placed in a 10 × 10 cm² electron applicator. These profile curves are obtained using parallel plane type ion chamber at the R₁₀₀, R₉₀, R₈₀ and R₅₀ depths. Correspondingly, the source surface distance is 100 cm.In this study MCNP Monte Carlo (MC) simulation was used to compare Percentage Depth Dose (PDD) and Profile of electron beams.Monte Carlo and measured results showed a good compliance for PDD and beam profile. The measurements and calculations showed that as the field width decreases, the Flatness and Penumbra Ratio also decreases. In other words, flatter plateau was available for larger fields. Also the Coverage Ratio for each of the profiles is presented. The flatness and symmetry values for triangle shapes were greater than the two other shapes.Knowledge of these changes are significant in radiation therapy. Accordingly, a comparison between the Monte Carlo data and the measured results can be beneficial for treatment simulation and development of treatment planning systems.     

Magnetic charge can locally stabilize Kaluza-Klein bubbles

We construct a new 2-parameter family of static topological solitons in 5D minimal supergravity which are endowed with magnetic charge and mass. The solitons are asymptotically R⁴×S¹, where the radius of the S¹ has a lower bound Rs?Rmin. Setting up initial data on a Cauchy slice at a moment of time symmetry, we demonstrate that if Rs>Rmin these solitons correspond to a perturbatively stable “small” static bubble as well as an unstable “large” static bubble, whereas if Rs<Rmin there are no static bubbles. The energetics and thermodynamics of the magnetic black string are then discussed and it is shown that the locally stable bubble is the end point of a phase transition for an appropriate range of black string parameters.     

Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres - except for two methods limited to narrow angle lidars - the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.     

Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within “small size” phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to t≈10⁶) by a q-Gaussian (1<q<3) distribution and tend to a Gaussian (q=1) for longer times, as the orbits eventually enter into “large size” chaotic domains. However, in agreement with other studies, we find in certain cases that the q-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called “crossover” function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these q-Gaussian distributions to identify two energy regimes of “weak chaos”—one where the system melts and one where it transforms from liquid to a gas state-by observing where the q-index of the distribution increases significantly above the q=1 value of strong chaos.     

Statistical and systematic errors in Monte Carlo sampling

We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the bin length (size of the statistical sample), both at and away from a phase transition. The formalism is tested using simulations of thed=3 Ising model at the infinite-lattice transition temperature. We show that for a 96×96×96 system noticeable systematic errors (systematic underestimation of response functions) are still present for total run lengths of 10⁶ Monte Carlo steps/site (MCS) with measurements taken at regular intervals of 10 MCS.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.     

Study of range distribution parameters for bismuth-ion implantation in silver gallium diselenide

Range distributions for bismuth ions implanted in AgGaSe₂ in the energy range 80–300 keV were investigated by using 2.1-MeV He²⁺ Rutherford backscattering spectrometry (RBS). A convolution calculation method was used to extract the true distributions of bismuth from the measured RBS spectra. The range distribution parameters, R_p and ΔR_p, were obtained and compared with those obtained from Monte Carlo simulation. The experimental R_p values agree with the Monte Carlo simulation values very well, but the experimental ΔR_p values are systematically larger than those from the theoretical simulation. Received: 28 January 2002 / Accepted: 11 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +86-531/856-5167, E-mail: xdliu@sdu.edu.cn     

Anomalous fluctuations in random walk dynamics

The anomalous dispersion of noninteracting particles randomly walking in a network is considered. It is shown that the existence of large dangling branches attached to a backbone induces a l/f-like behavior in the current autocorrelation function at low frequencies. The waiting times associated with dangling loops scale liket ^–3/2. The size of the dangling branches provides a lower cutoff to the power law behavior. When the side branches are infinite, self-similar structures, the power law behavior persists up to a zero frequency. The currents we consider are created either by a bias on the random walk or by a current source. We consider both the total current, which is often referred to in the literature, and the current measured at endpoints of a specimen attached to a (model) battery. The differences and similarities between the two corresponding correlations are analyzed. In particular, we find that in the second case l/f noise exists only for large bias. When a statistical distribution of dangling branches is considered, we find that the largest power of frequency in the spectrum is 1.13. Much of our results are true when the dangling branches are replaced by traps having waiting time distributions that equal those of the branches. The waiting time associated with a power law distribution of dangling loops (m ^–x:m is the length of the loop) scales liket ^–1 –(x/2). However, it is shown that geometry alone can be responsible for the appearance of power laws in the spectra. Random geometry can be regarded as a model (or source) of random hopping times.     

CARS spectral fitting with multiple resonant species using sparse libraries

The coherent anti‐Stokes Raman spectroscopy (CARS) technique is often used in the study of turbulent flames. Fast and accurate algorithms are needed for fitting CARS spectra for temperature and multiple chemical species. This paper describes the development of such an algorithm. The algorithm employs sparse libraries whose size grows more slowly with number of species than a regular library. It was demonstrated by fitting synthetic ‘experimental’ dual‐pump CARS spectra containing four resonant species (N₂, O₂, H₂ and CO₂), both with added noise and without it, and by fitting experimental spectra from a H₂ air flat flame produced by a Hencken burner. In the four‐species example, the library was nearly an order of magnitude smaller than the equivalent regular library (fitting times are correspondingly faster), and the fitting errors in the absence of added noise were negligible compared to the random errors associated with fitting noisy spectra. When fitting noisy spectra, weighted least squares fitting to signal intensity, as opposed to least squares fitting or least squares fitting to square root of intensity, minimized random and bias errors in fit parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Compensation of nonlinear phase noise in an in-plane-magnetized anisotropic spin-torque oscillator

A theory of generation linewidth of a spin-torque oscillator (STO) based on an in-plane-magnetized nano-pillar with an anisotropic “free” magnetic layer has been developed. It is predicted that by choosing the direction of the in-plane bias magnetic field H₀ along the “hard” anisotropy axis of the STO “free” layer and the magnitude of this field to be four times larger than the anisotropy field H_A (H₀=4H_A) it would be possible to compensate the nonlinear phase noise and to achieve the minimum value of the generation linewidth, characteristic for an auto-oscillator without a nonlinear frequency shift.     

Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate R is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when R is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on R.     

Un-graviton corrections to the Schwarzschild black hole

We introduce an effective action smoothly extending the standard Einstein–Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original “guess” of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and “dressing” the Newtonian potential with un-gravitons, we solve the “effective Einstein equations” including all order un-gravity effects. An unexpected “bonus” of accounting un-gravity effects is the fractalisation   of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension dU$d_U$.     

Effects of interactions among wave aberrations on optical image quality after refractive surgery

Research on wave aberrations indicates that interactions and balances among aberrations can provide better visual quality for normal eyes. In this paper, we investigate the aberration compensatory mechanism for eyes after LASIK surgery. Data of Zernike coefficients of wave-front aberrations are collected from 60 post-operative eyes through a Hartmann-Shack wave-front sensor, and then a series of Monte Carlo simulations are performed by manipulating the value of each Zernike coefficient (second order through seventh order). The modulation transfer function (MTF) ratio as a function of spatial frequency is used to evaluate the aberrations’ characteristic of independence. Finally, in a control condition, “synthetic” model eyes are produced through Monte Carlo arithmetic and the aberration independence of the synthetic eyes is analyzed. The results suggest that, for 6 and 3 mm pupil size, aberrations of the eyes after LASIK surgery are still not independent and the adaptive mechanism still exists. However, the adaptive mechanism does not hold for the “synthetic” eyes.     

Line mixing in the ν6Q branches of self- and nitrogen-broadened methyl bromide

Line-mixing effects are studied in the ν₆^RQ_K and ^PQ_K (K=0-6) branches of methyl bromide (CH₃Br) perturbed by nitrogen (N₂). Laboratory Fourier transform spectra have been obtained at room temperature, and for a large range of pressure values of atmospheric interest. In order to accurately model these spectra, a theoretical approach accounting for line-mixing effects is proposed. This model is based on the use of the state-to-state rotational cross-sections calculated by a statistical modified exponential-gap fitting law depending on a few empirical parameters. These parameters are deduced by adjusting the calculated diagonal elements of the relaxation matrix to the N₂-broadening coefficients, known from accurate previous measurements. Comparisons between experimental and calculated profiles for various Q branches and under various pressure conditions (0.2-1 atm) demonstrate the adequacy and consistency of the proposed model. To allow accurate laboratory measurements, line-mixing effects are also modeled in the case of self-perturbed CH₃Br.     

Monte Carlo Effective Hamiltonian in 1+1 Dimensional Case'

Using a recently developed Monte Carlo effective Hamiltonian method,we study the low energy physics of 1+1 dimensional quantum mechanical system V(x)=μ²x²+λx⁴(here μ²<0,λ>0),which is similar to Higgs potential in the standard model of unified electroweak theory.Good results of the spectra,wavefunctions and thermodynamical observables are obtained.It shows that the new Monte Carlo Hamiltonian method has potential application to systems with many degrees of freedom and lattice gauge theory.     

Natural frequency intervals for vibrating systems with polytopic uncertainty

We consider the problem of locating the natural frequencies of uncertain systems whose describing matrices are functions of an unknown parameter vector which is included in an assigned bounding set. We face what we call the weak frequency interval detection problem of determining the smallest interval which includes all possible frequencies. We show that if the system matrices depend affinely on the parameter vector, whose bounding set is a compact polyhedron, then this problem requires the solution of a finite number of eigenvalue problems associated with the vertices of such a polyhedron. Unfortunately, detecting the intervals associated with all the natural frequencies (strong frequency interval detection problem), cannot rely on this property, so that one must resort to Monte Carlo methods or numerical optimization to find them. We show that the strong version is solvable “exploring the vertices only” under some stronger assumptions. In the case in which the uncertainty bounding set is not defined by linear inequalities, not even the extremal frequencies can be associated with the vertices of the admissibility domain. Then again, numerical approach is necessary unless we accept to merge the original system in a larger one of an “affine nature”. Finally, we present as an application the study of structures with uncertain mass distribution.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

The nano-structural properties of hydrogenated a-Si and Si-C thin films alloys by GISAXS and vibrational spectroscopy

Amorphous hydrogenated silicon (a-Si:H) with high hydrogen content (10-40 at.%), and non-stehiometric silicon-carbon (Si_1−xC_x) thin films with a variation of the carbon to silicon ratio up to 0.3, were deposited by using a magnetron sputtering source. The Si_1−xC_x thin films were partially crystallised after deposition by thermal annealing up to 1050 °C.The GISAXS (Grazing Incidence Small Angle X-ray Scattering) spectra of all of the prepared specimens indicate the presence of “particles” in the “bulk” of the films. For the a-Si:H samples, “particles” are most probably voids agglomerates with a variation in size between 3 and 6 nm. The mean value of the size distribution of the “particles” increases while its width slightly decreases with the hydrogen content in the film. This indicates a better structural ordering which is consistent with the results of Raman spectroscopy that show a decrease of the ratio between intensities of transversal acoustic (TA) and transversal optic (TO) phonon peaks, I_TA/I_TO, and a narrowing of the TO peak with increasing hydrogen content. These results are discussed as a consequence of the beneficial influence of hydrogen bombardment during the film growth.For Si_1−xC_x thin films, the “particles” are assumed to be SiC nano-crystals with a size between 2 and 14 nm and they are larger in films with a higher carbon concentration. Inside each of the films, the crystals are larger closer to surface and they grow faster in the direction parallel to the surface than in that which is perpendicular to it.