Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator

One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.

On the Innovation,Design,Construction,and Experiments of OMEGA-Based SSPS Prototype:The Sun-Chasing Project

This study systematically introduces the development of the world’s first full-link and full-system ground demonstration and verification system for the OMEGA space solar power satellite(SSPS).First,the OMEGA 2.0 innovation design was proposed.Second,field-coupling theoretical models of sunlight concentration,photoelectric conversion,and transmitting antennas were established,and a systematic optimization design method was proposed.Third,a beam waveform optimization methodology considering both a high beam collection efficiency and a circular stepped beam shape was proposed.Fourth,a control strategy was developed to control the condenser pointing toward the sun while maintaining the transmitting antenna toward the rectenna.Fifth,a high-efficiency heat radiator design method based on bionics and topology optimization was proposed.Sixth,a method for improving the rectenna array’s reception,rectification,and direct current(DC)power synthesis efficiencies is presented.Seventh,high-precision measurement technology for high-accuracy beam-pointing control was developed.Eighth,a smart mechanical structure was designed and developed.Finally,the developed SSPS ground demonstration and verification system has the capacity for sun tracking,a high concentration ratio,photoelectric conversion,microwave conversion and emission,microwave reception,and rectification,and thus satisfactory results were obtained.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Variational quantum simulation of the quantum critical regime

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.

Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC： an overview

Fluctuations of conserved quantities, such as baryon, electric charge, and strangeness number, are sensitive observables in relativistic heavy-ion collisions to probe the QCD phase transition and search for the QCD critical point. In this paper, we review the experimental measurements of the cumulants(up to fourth order) of event-byevent net-proton(proxy for net-baryon), net-charge and netkaon(proxy for net-strangeness) multiplicity distributions Au+Au collisions at sNN^(1/2) 7:7; 11:5; 14:5; 19:6; 27;39; 62:4; 200 Ge V from the first phase of beam energy scan program at the relativistic heavy-ion collider(RHIC). We also summarize the data analysis methods of suppressing the volume fluctuations, auto-correlations, and the unified description of efficiency correction and error estimation.Based on theoretical and model calculations, we will discuss the characteristic signatures of critical point as well as backgrounds for the fluctuation observables in heavy-ion collisions. The physics implications and the future secondphase of the beam energy scan(2019–2020) at RHIC will also be discussed.

Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach

The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pioneer as well as in more recent literature to exhibit all kinds of distinct critical points. Its response is thoroughly discussed, the effect of all parameters involved is extensively examined, including imperfection sensitivity, and the results obtained lead to the important conclusion that the model is possibly associated with the butterfly singularity, a fact which will be validated by the contents of a companion paper, based on catastrophe theory.

ON THE CRITICAL POINTS OF THE MAP F_p:X→‖AXB-C‖_p^p

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.

Distinction between critical current effects and intrinsic anomalies in the point-contact Andreev reflection spectra of unconventional superconductors

In this work,we discuss the origin of several anomalies present in the point-contact Andreev reflection spectra of（Li1-xFex）OHFeSe,LiTi2O4,and La2-xCexCuO4.While these features are similar to those stemming from intrinsic superconducting properties,such as Andreev reflection,electron-boson coupling,multigap superconductivity,d-wave and p-wave pairing symmetry,they cannot be accounted for by the modified Blonder–Tinkham–Klapwijk（BTK） model,but require to consider critical current effects arising from the junction geometry.Our results point to the importance of tracking the evolution of the dips and peaks in the differential conductance as a function of the bias voltage,in order to correctly deduce the properties of the superconducting state.

Analysis of Microbial Contamination Factors and Critical Control Points in the Process of Hog Slaughter and Production

In order to provide a reference for the further study of microbial contamination in the pork production process. Microbial contamination of pigs came from three slaughterhouses were detected, and critical control points in the progress of hog slaughter and processing were analyzed. The results showed that microbial con- taminatian existed in the entire slaughter and processing progress, including shower and assassination bloodletting, separation of the internal organs, chopping boards, workshop environment, personal hygiene of the operators, etc. , which should be paid more attention to. The results indicated that reasonable protection measures should be carried out, disinfection awareness of the operators should be improved, and regular disinfection should be ruled under the condition of continu- ous operation.

Fluid phases of argon: A debate on the absence of van der Waals’ “critical point”

A phase diagram of argon based upon percolation transition loci determined from literature experimental p-V isotherms, and simulation values using a Lennard-Jones model shows three fluid phases. The liquid phase spans all temperatures, from a metastable amorphous ground state at 0K, to ultra-high T. There is a supercritical mesophase bounded by percolation transition loci, and a gas phase. Intersection of two percolation loci in the p-T plane thermodynamically defines a critical line between two coexisting gas and liquid critical states at T = Tc, and the single mesophase for T > Tc. A debate on the absence of a van der Waals critical point in the Gibbs p-T density surface is appended.

Dynamical signatures of the one-dimensional deconfined quantum critical point

We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.

ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.

Carbon,nitrogen and phosphorus coupling relationships and their influencing factors in the critical zone of Dongting Lake wetlands,China

Wetland is a transition zone between terrestrial and aquatic ecosystems,and is the source and sink of various biogenic elements in the earth’s epipelagic zone.In order to investigate the driving force and coupling mechanism of carbon(C),nitrogen(N)and phosphorus(P)migration in the critical zone of lake wetland,this paper studies the natural wetland of Dongting Lake area,through measuring and analysing the C,N and P contents in the wetland soil and groundwater.Methods of Pearson correlation,non-linear regression and machine learning were employed to analyse the influencing factors,and to explore the coupling patterns of the C,N and P in both soils and groundwater,with data derived from soil and water samples collected from the wetland critical zone.The results show that the mean values of organic carbon(TOC),total nitrogen(TN)and total phosphorus(TP)in groundwater are 1.59 mg/L,4.19 mg/L and 0.5 mg/L,respectively,while the mean values of C,N and P in the soils are 18.05 g/kg,0.86 g/kg and 0.52 g/kg.The results also show that the TOC,TN and TP in the groundwater are driven by a variety of environmental factors.However,the concentrations of C,N and P in the soils are mainly related to vegetation abundance and species which influence each other.In addition,the fitted curves of wetland soil C-N and C-P appear to follow the power function and S-shaped curve,respectively.In order to establish a multivariate regression model,the soil N and P contents were used as the input parameters and the soil C content used as the output one.By comparing the prediction effects of machine learning and nonlinear regression modelling,the results show that coupled relationship equation for the C,N and P contents is highly reliable.Future modelling of the coupled soil and groundwater elemental cycles needs to consider the complexity of hydrogeological conditions and to explore the quantitative relationships among the influencing factors and chemical constituents.

Stability Analysis of a SDOF Mechanical Model with Distinct Critical Points: II. Catastrophe Theory Approach

In a recent publication [1], the fully nonlinear stability analysis of a Single-Degree-of Freedom (SDOF) model with distinct critical points was dealt with on the basis of bifurcation theory, and it was demonstrated that this system is associated with the butterfly singularity. The present work is the companion one, tackling the problem via the Theory of Catastrophes. After Taylor expanding the original potential energy function and introducing Padè approximants of the trigonometric expression involved, the resulting truncated potential is a universal unfolding of the original one and an extended canonical form of the butterfly catastrophe potential energy function. Results in terms of equilibrium paths, bifurcation sets and manifold hyper-surface projections fully validate the whole analysis, being in excellent agreement with the findings obtained via bifurcation theory.

Update on point of care ultrasound in the care of the critically ill patient

One of the most exciting developments to come to the aid of the critically ill patient in recent years is not new at all, but rather has been repackaged and evolved to a level where point-of-care use by critical care physicians has been made possible. Critical care or point-of-care ultrasound dates back more than twenty years, but has come to prominence in the last 5 years and is spreading quickly. Multiple critical care societies have taken up ultrasound policy and training and one organization has been formed that concentrates only on point-of-care ultrasound in critical settings and interventions. The amount of literature generated on the topic is increasing rapidly and hardly a major clinical journal exists that has not published ultrasound related topics.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

The December 26, 2004, off the west coast of northern Sumatra, Indonesia, M_W=9.0, earthquake and the critical-point-like model of earthquake preparation

Long-term seismic activity prior to the December 26, 2004, off the west coast of northern Sumatra, Indonesia, MW=9.0 earthquake was investigated using the Harvard CMT catalogue. It is observed that before this great earth-quake, there exists an accelerating moment release (AMR) process with the temporal scale of a quarter century and the spatial scale of 1 500 km. Within this spatial range, the MW=9.0 event falls into the piece-wise power-law-like frequency-magnitude distribution. Therefore, in the perspective of the critical-point-like model of earthquake preparation, the failure to forecast/predict the approaching and/or the size of this earthquake is not due to the physically intrinsic unpredictability of earthquakes.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.