Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λn(L, t) = Lγ/νf n(t L^(1/ν)), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ1, λ2 and λ6, we get the finite-size scaling form of the second moment correlation length ξ(L, t) = Lξ(tL^(1/ν)).It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|^(-(d-2+η))and a finite-size scaling function of the variables r/L and tL^(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.

State of the art of synthetic threshold scale inhibitors for mineral scaling in the petroleum industry: a review

Inorganic scale deposits are a major water-related problem encountered in producing oil and gas wells. The harshness of scale deposits is dependent on the field operating conditions. Scale deposits can vary from mild scaling tendencies to extreme. In general, the scale deposit will cause a reduction in formation pores, declining productivity and eventually blockage of the wellbore and hence unexpected downtime if it is allowed to persevere. To overcome this, the productivity of an oil and gas well is ensured by handling scale deposits via removal or prevention methods. Scale prevention is the best and cost-e ective method for handling scale deposits that ensures production continuity. Inhibition through 'threshold' scale inhibitor treatment is the most common method that is proven to prevent or reduce likely deposits. This paper examines the art of synthetic scale inhibitors, in particular, threshold scale inhibitors in oil and gas production. It discusses the chemistry of those inhibitors, inhibition mechanisms, treatment methods and key properties for their applications. It also highlights the chemistry of the synthetic routes often used to produce them in the laboratory and/or industry. Finally, it highlights the environmental concerns for the applicability of threshold scale inhibitors.

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.

The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling of the Planck Scale

The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.

基于多尺度Scale-Unet的单样本图像翻译

随着生成对抗网络(GAN)的发展,基于单样本的无监督图像到图像翻译(UI2I)取得了重大进展。然而,以前方法无法捕获图像中的复杂纹理并保留原始内容信息。为解决这个问题,提出了一种基于尺度可变U-Net结构(Scale—Unet)的新型单样本图像翻译结构SUGAN。所提出的SUGAN使用Scale—Unet作为生成器,利用多尺度结构和渐进方法不断改进网络结构,以从粗到细地学习图像特征。同时,提出了尺度像素损失scale-pixel来更好地约束保留原始内容信息,防止信息丢失。实验表明,与SinGAN、TuiGAN、TSIT、StyTR2等公共数据集Summer■Winter、Horse■Zebra上的方法相比,该方法生成图像的SIFID值平均降低了30%。所提方法可更好地保留图像内容信息,同时生成详细逼真的高质量图像。

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.

Scaling parameters selection principle for the scaled unscented Kalman filter

The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

Finite-size analysis of continuous-variable quantum key distribution with entanglement in the middle

Continuous-variable quantum key distribution(CVQKD) protocols with entanglement in the middle(EM) enable long maximal transmission distances for quantum communications. For the security analysis of the protocols, it is usually assumed that Eve performs collective Gaussian attacks and there is a lack of finite-size analysis of the protocols. However,in this paper we consider the finite-size regime of the EM-based CVQKD protocols by exposing the protocol to collective attacks and coherent attacks. We differentiate between the collective attacks and the coherent attacks while comparing asymptotic key rate and the key rate in the finite-size scenarios. Moreover, both symmetric and asymmetric configurations are collated in a contrastive analysis. As expected, the derived results in the finite-size scenarios are less useful than those acquired in the asymptotic regime. Nevertheless, we find that CVQKD with entanglement in the middle is capable of providing fully secure secret keys taking the finite-size effects into account with transmission distances of more than 30 km.

Assessment of force models on finite-sized particles at finite Reynolds numbers

Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method(IBPM)in the turbulent open-channel flow by direct numerical simulation(DNS).The accuracy of the particle surface force models is investigated in comparison with the total force obtained via the fully-resolved method.The results show that the steady-state resistance only performs well in the streamwise direction,while the fluid acceleration force,the added-mass force,and the shear-induced Saffman lift can effectively compensate for the large-amplitude and high-frequency characteristics of the particle surface forces,especially for the wall-normal and spanwise components.The modified steady-state resistance with the correction effects of the acceleration and the fluid shear can better represent the overall forces imposed on the particles,and it is a preferable choice of the surface force model in the Lagrangian point-particle method.

Transition and self-sustained turbulence in dilute suspensions of finite-size particles

We study the transition to turbulence of channel flow of finite-size particle suspensions at low volume fraction, i.e., φ ≈0.001. The critical Reynolds number above which turbulence is sustained reduces to Re ≈ 1675, in the presence of few particles, independently of the initial condition, a value lower than that of the corresponding single-phase flow, i.e., Re ≈1775. In the dilute suspension, the initial arrangement of the particles is important to trigger the transition at a fixed Reynolds number and particle volume fraction. As in single phase flows, streamwise elongated disturbances are initially induced in the flow. If particles can induce oblique disturbances with high enough energy within a certain time, the streaks breakdown, flow experiences the transition to turbulence and the particle trajectories become chaotic, Otherwise, the streaks decay in time and the particles immigrate towards the channel core in a laminar flow.

EXTENDED SELF-SIMILAR SCALING LAW OF MULTI-SCALE EDDY STRUCTURE IN WALL TURBULENCE

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Effects of finite-size neutrally buoyant particles on the turbulent channel flow at a Reynolds number of 395

A direct-forcing fictitious domain(DFFD) method is used to perform fully resolved numerical simulations of turbulent channel flows laden with large neutrally buoyant particles. The effects of the particles on the turbulence(including the mean velocity,the root mean square(RMS) of the velocity fluctuation, the probability density function(PDF) of the velocity, and the vortex structures) at a friction Reynolds number of 395 are investigated. The results show that the drag-reduction effect caused by finite-size spherical particles at low particle volumes is negligibly small. The particle effects on the RMS velocities at Re_τ = 395 are significantly smaller than those at Re_τ = 180, despite qualitatively the same effects, i.e., the presence of particles decreases the maximum streamwise RMS velocity near the wall via weakening the large-scale streamwise vortices,and increases the transverse and spanwise RMS velocities in the vicinity of the wall by inducing smaller-scale vortices. The effects of the particles on the PDFs of the fluid fluctuating velocities normalized with the RMS velocities are small, regardless of the particle size, the particle volume fraction, and the Reynolds number.

Finite-size analysis of eight-state continuous-variable quantum key distribution with the linear optics cloning machine

We propose a method to improve the secret key rate of an eight-state continuous-variable quantum key distribution（CVQKD） by using a linear optics cloning machine（LOCM）. In the proposed scheme, an LOCM is exploited to compensate for the imperfections of Bob＇s apparatus, so that the generated secret key rate of the eight-state protocol could be well enhanced. We investigate the security of our proposed protocol in a finite-size scenario so as to further approach the practical value of a secret key rate. Numeric simulation shows that the LOCM with reasonable tuning gain λ and transmittance τcan effectively improve the secret key rate of eight-state CVQKD in both an asymptotic limit and a finite-size regime.Furthermore, we obtain the tightest bound of the secure distance by taking the finite-size effect into account, which is more practical than that obtained in the asymptotic limit.

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks.A real space complete condensation phase transition in the stationary state may occur.We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks.By means of grand canonical ensemble method,we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state.We further explore the relaxation dynamics of the condensation phase transition.By applying the hierarchical evolution and scaling ansatz,a scaling law for the relaxation dynamics is predicted.Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

Exploring the mechanisms of calcium carbonate deposition on various substrates with implications for effective anti-scaling material selection

The unexpected scaling phenomena have resulted in significant damages to the oil and gas industries,leading to issues such as heat exchanger failures and pipeline clogging.It is of practical and fundamental importance to understand the scaling mechanisms and develop efficient anti-scaling strategies.However,the underlying surface interaction mechanisms of scalants(e.g.,calcite)with various substrates are still not fully understood.In this work,the colloidal probe atomic force microscopy(AFM)technique has been applied to directly quantify the surface forces between calcite particles and different metallic substrates,including carbon steel(CR1018),low alloy steel(4140),stainless steel(SS304)and tungsten carbide,under different water chemistries(i.e.,salinity and pH).Measured force profiles revealed that the attractive van der Waals(VDW)interaction contributed to the attachment of the calcium carbonate particles on substrate surfaces,while the repulsive electric double layer(EDL)interactions could inhibit the attachment behaviors.High salinity and acidic p H conditions of aqueous solutions could weaken the EDL repulsion and promote the attachment behavior.The adhesion of calcite particles with CR1018 and4140 substrates was much stronger than that with SS304 and tungsten carbide substrates.The bulk scaling tests in aqueous solutions from an industrial oil production process showed that much more severe scaling behaviors of calcite was detected on CR1018 and 4140 than those on SS304 and tungsten carbide,which agreed with surface force measurement results.Besides,high salinity and acidic p H can significantly enhance the scaling phenomena.This work provides fundamental insights into the scaling mechanisms of calcite at the nanoscale with practical implications for the selection of suitable antiscaling materials in petroleum industries.

Uncertainties of landslide susceptibility prediction:influences of different study area scales and mapping unit scales

This study aims to investigate the effects of different mapping unit scales and study area scales on the uncertainty rules of landslide susceptibility prediction(LSP).To illustrate various study area scales,Ganzhou City in China,its eastern region(Ganzhou East),and Ruijin County in Ganzhou East were chosen.Different mapping unit scales are represented by grid units with spatial resolution of 30 and 60 m,as well as slope units that were extracted by multi-scale segmentation method.The 3855 landslide locations and 21 typical environmental factors in Ganzhou City are first determined to create spatial datasets with input-outputs.Then,landslide susceptibility maps(LSMs)of Ganzhou City,Ganzhou East and Ruijin County are pro-duced using a support vector machine(SVM)and random forest(RF),respectively.The LSMs of the above three regions are then extracted by mask from the LSM of Ganzhou City,along with the LSMs of Ruijin County from Ganzhou East.Additionally,LSMs of Ruijin at various mapping unit scales are generated in accordance.Accuracy and landslide suscepti-bility indexes(LSIs)distribution are used to express LSP uncertainties.The LSP uncertainties under grid units significantly decrease as study area scales decrease from Ganzhou City,Ganzhou East to Ruijin County,whereas those under slope units are less affected by study area scales.Of course,attentions should also be paid to the broader representativeness of large study areas.The LSP accuracy of slope units increases by about 6%–10%compared with those under grid units with 30 m and 60 m resolution in the same study area's scale.The significance of environmental factors exhibits an averaging trend as study area scale increases from small to large.The importance of environmental factors varies greatly with the 60 m grid unit,but it tends to be consistent to some extent in the 30 m grid unit and the slope unit.

Complete Universal Scaling in First-Order Phase Transitions

Phase transitions and critical phenomena are among the most intriguing phenomena in nature and society.They are classified into first-order phase transitions(FOPTs)and continuous ones.While the latter shows marvelous phenomena of scaling and universality,whether the former behaves similarly is a long-standing controversial issue.Here we definitely demonstrate complete universal scaling in field driven FOPTs for Langevin equations in both zero and two spatial dimensions by rescaling all parameters and subtracting nonuniversal contributions with singular dimensions from an effective temperature and a special field according to an effective theory.This offers a perspective different from the usual nucleation and growth but conforming to continuous phase transitions to study FOPTs.

基于分数阶傅里叶变换和图像加权熵的chirp scaling算法

针对传统的基于傅里叶变换和匹配滤波实现的chirp scaling(CS)成像算法中多普勒参数随斜距变化以及成像分辨率低的问题,提出利用分数阶傅里叶变换(FRFT)对CS成像算法进行优化。首先建立斜视合成孔径雷达(SAR)回波信号模型,理论推导利用FRFT代替匹配滤波进行信号压缩。针对方位向最优旋转角的搜索问题,对得到的图像基于加权最小熵建立代价函数,利用动量法的梯度下降优化算法进行迭代计算,最终得到分辨率更高的SAR图像。为验证算法的有效性,分别在点目标仿真数据和实测SAR数据集上进行实验。结果表明,与传统CS成像算法相比,该算法的成像结果成像主瓣宽度更窄、旁瓣更低、成像更加清晰。

Rate-limiting factors in hydrate decomposition through depressurization across various scales:A mini-review

Natural gas hydrate is an energy resource for methane that has a carbon quantity twice more than all traditional fossil fuels combined.However,their practical application in the field has been limited due to the challenges of long-term preparation,high costs and associated risks.Experimental studies,on the other hand,offer a safe and cost-effective means of exploring the mechanisms of hydrate dissociation and optimizing exploitation conditions.Gas hydrate decomposition is a complicated process along with intrinsic kinetics,mass transfer and heat transfer,which are the influencing factors for hydrate decomposition rate.The identification of the rate-limiting factor for hydrate dissociation during depressurization varies with the scale of the reservoir,making it challenging to extrapolate findings from laboratory experiments to the actual exploitation.This review aims to summarize current knowledge of investigations on hydrate decomposition on the subject of the research scale(core scale,middle scale,large scale and field tests)and to analyze determining factors for decomposition rate,considering the various research scales and their associated influencing factors.