The conventional point-particle approach for treating the dispersed phase in a continuous flowfield is extended by taking into account the effect of finite particle size, using a Gaussian interpolation from Lagrangian...The conventional point-particle approach for treating the dispersed phase in a continuous flowfield is extended by taking into account the effect of finite particle size, using a Gaussian interpolation from Lagrangian points to the Eulerian field.The inter-phase exchange terms in the conservation equations are distributed over the volume encompassing the particle size, as opposed to the Dirac delta function generally used in the point-particle approach.The proposed approach is benchmarked against three different flow configurations in a numerical framework based on large eddy simulation（LES） turbulence closure.First, the flow over a circular cylinder is simulated for a Reynolds number of 3900 at 1 atm pressure.Results show good agreement with experimental data for the mean streamwise velocity and the vortex shedding frequency in the wake region.The calculated flowfield exhibits correct physics, which the conventional point-particle approach fails to capture.The second case deals with diesel jet injection in quiescent environment over a pressure range of 1.1–5.0 MPa.The calculated jet penetration depth closely matches measurements.It decreases with increasing chamber pressure, due to enhanced drag force in a denser fluid environment.Finally, water and acetone jet injection normal to air crossflow is studied at1 atm.The calculated jet penetration and Sauter mean diameter of liquid droplets compare very well with measurements.展开更多
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 wi...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.展开更多
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 i...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.展开更多
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 surfac...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.展开更多
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 ≈ 167...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.展开更多
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 turb...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.展开更多
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 princi...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.展开更多
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...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.展开更多
While non-Hermiticity provokes intriguing phenomena without Hermitian counterparts, e.g., the skin effect and the breakdown of bulk-boundary correspondence, attracting extensive attention both in fundamental physics a...While non-Hermiticity provokes intriguing phenomena without Hermitian counterparts, e.g., the skin effect and the breakdown of bulk-boundary correspondence, attracting extensive attention both in fundamental physics and device engineering, the role of finite sizes therein remains elusive. Here, we propose a class of finite-size-induced non-Hermitian phase transitions, relying upon higher-order topological invariants associated with real-space wave functions. The phase diagrams for general non-Hermitian chiral models are further acquired to demonstrate our topological definition. Such phase transitions are elucidated qualitatively by an effective intercell coupling alteration that depends on finite sizes in respective directions. Besides, we mimic these phenomena by analogizing the circuit Laplacian in finite-size electric circuits with nonreciprocal couplings. The resultant admittance spectra agree with our theoretical predictions. Our findings shed light on the finite-size mechanism of non-Hermitian topological phase transitions and pave the way for applications in switching and sensing.展开更多
The influences of finite-size effects on the self-organized criticality (SOC) of the traditional forest-fire model are investigated by means of a new method. The forest size is originally set to a value much greater t...The influences of finite-size effects on the self-organized criticality (SOC) of the traditional forest-fire model are investigated by means of a new method. The forest size is originally set to a value much greater than the correla-tion length of the forest. Finite-size effects are then studied by equally dividing the forest into more and more separate subsystems on condition that the forest size, igniting prob-ability and planting probability are invariant. A new phe-nomenon, i.e. the finite-size effects with one-side frequency peak, is observed. The boundary between two neighboring subsystems can be regarded as a firebreak. The concept of ’separation ability’ is introduced to represent the probability for the firebreak to block off the fire successfully. Restrain-ing effects of separation ability on finite-size effects are ana-lyzed. Finite-size effects and separation ability, as well as their relations are found to have practical importance to the actual forest-fire protection.展开更多
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...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.展开更多
We perform a comprehensive study of the electron-doped t-t′-J model on cylinders with density matrix renormalization group(DMRG).We conduct a systematic study on the finite-size and boundary condition effects on t-t...We perform a comprehensive study of the electron-doped t-t′-J model on cylinders with density matrix renormalization group(DMRG).We conduct a systematic study on the finite-size and boundary condition effects on t-t′-J model on cylinders.Periodic and anti-periodic boundary conditions are implemented along the circumference direction,with the system’s width extending up to as large as 8 lattice units.We study doping levels of 1/6,1/8,and 1/12,which represent the most interesting region in the phase diagram of electron-doped cuprates.We find that for width-4 and width-6 systems,the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and system widths,indicating the presence of large finite size effect in the t-t′-J model.We also have a careful analysis of the d-wave pairing correlations which also change quantitatively with boundary conditions and widths of the system.However,the pairing correlations are enhanced when the system becomes wider for all dopings,suggesting the existence of possible long-range superconducting order in the thermodynamic limit.The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach.For the width-8 system,only Neel(stripe)state can be stabilized in DMRG calculation for 1/12(1/6)doping,while both stripe and Neel states are stable in the DMRG sweep for 1/8 doping,regardless of the boundary conditions.These results indicate that 1/8 doping is likely to lie on the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping,consistent with the previous study.The sensitivity of the ground state on boundary conditions and size observed for narrow systems is similar to that found in the t′-Hubbard model,where the t′term introduces frustration and makes the stripe state fragile.The study of different boundary conditions provides a useful tool to check the finite size effect in the future DMRG calculations.展开更多
The sign of higher-order multiplicity fluctuations is a very important parameter for exploring QCD phase transitions.The kurtosis of the net-baryon is typically negative in simulations of the dynamics of the conserved...The sign of higher-order multiplicity fluctuations is a very important parameter for exploring QCD phase transitions.The kurtosis of the net-baryon is typically negative in simulations of the dynamics of the conserved net-baryon density near the QCD critical point.This paper considers the effects of finite size on multiplicity fluctuations with equilibrium critical fluctuations.It is found that the multiplicity fluctuations(or the magnitude of the correlation function D_(ij))are dramatically suppressed with decreasing system size when the size of the system is small compared with the correlation length,which is the so-called acceptance dependence.Consequently,the small correlation function of the small system size results in the magnitude of the negative contribution(~D_(ij)^(4))in the four-point correlation function dominating the positive term(~D_(ij)^(5)),and this finite-size effect induces a dip structure near the QCD critical point.展开更多
Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement fiel...Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.展开更多
The pore configuration in porous medium is assumed to be the randomly distributed cube-like particles which can overlap each other in the periodic cubic domain, and the impact of particle characteristics on the percol...The pore configuration in porous medium is assumed to be the randomly distributed cube-like particles which can overlap each other in the periodic cubic domain, and the impact of particle characteristics on the percolation property of these cube-like particle packing systems is analyzed.Firstly, by combining the percolation models and finite-size scaling analysis, three numerical parameters(i.e., percolation transition width △L, local percolation threshold ψ_c(L), and correlation length exponent v) for the cube-like particle systems with shape parameter s in[1.0, +∞] are derived successively. Then, based on the relation between the percolation thresholdψ_c in infinite space and the local percolation threshold ψ_c(L), the corresponding ψ_c with s in[1.0, +∞] are further determined. It is shown from the study that the characteristics of cube-like particles have significant influence on the global percolation threshold ψ_c of the particle packing systems. As the parameter s increases from 1.0 to +∞, the percolation threshold ψ_c will go down persistently. When the surface of cube-like particles is cubical and spherical, respectively, the minimum and maximum thresholds ψ_c,min and ψ_c,max are obtained.展开更多
A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A ...A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.展开更多
In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J0 J1 J2 model, which corresponds to t...In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J0 J1 J2 model, which corresponds to the staggered j-j′ model on a square lattice and a honeycomb lattice when J1/J0 equals 1 and O, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J1/J0 changing from 0 to 1 as a function of coupling ratio a = J2/J0. We extract all the critical values of the coupling ratio ac for these models, and we also obtain the critical exponents v,β/ν, and η using different finite-size scaling ansatz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum ciriteial points in these models.展开更多
We present a three-party reference frame independent quantum key distribution protocol which can be implemented without any alignment of reference frames between the sender and the receiver.The protocol exploits entan...We present a three-party reference frame independent quantum key distribution protocol which can be implemented without any alignment of reference frames between the sender and the receiver.The protocol exploits entangled states to establish a secret key among three communicating parties.We derive the asymptotic key rate for the proposed protocol against collective attacks and perform a finite-size key security analysis against general attacks in the presence of statistical fluctuations.We investigate the impact of reference frame misalignment on the stability of our protocol,and we obtain a transmission distance of 180 km,200 km,and 230 km for rotation of reference framesβ=π/6,β=π/8 andβ=0,respectively.Remarkably,our results demonstrate that our proposed protocol is not heavily affected by an increase in misalignment of reference frames as the achievable transmission distances are still comparable to the case where there is no misalignment in reference frames(whenβ=0).We also simulate the performance of our protocol for a fixed number of signals.Our results demonstrate that the protocol can achieve an effective key generation rate over a transmission distance of about 120 km with realistic 107 finite data signals and approximately achieve 195 km with 109 signals.Moreover,our proposed protocol is robust against noise in the quantum channel and achieves a threshold error rate of 22.7%.展开更多
Through using the methods of finite-size effect and short time dynamic scaling,we study the criticalbehavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment.Thr...Through using the methods of finite-size effect and short time dynamic scaling,we study the criticalbehavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment.Throughcomprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition fromdisease-free state to endemic state with a finite population density.We determine the critical population density,abovewhich the system reaches an epidemic spreading stationary state.We also perform a scaling analysis to determine theorder parameter and critical relaxation exponents.The results show that the model does not belong to the usual directedpercolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.展开更多
Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attr...Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.展开更多
基金sponsored by the William R.T.Oakes Endowment of the Georgia Institute of Technology
文摘The conventional point-particle approach for treating the dispersed phase in a continuous flowfield is extended by taking into account the effect of finite particle size, using a Gaussian interpolation from Lagrangian points to the Eulerian field.The inter-phase exchange terms in the conservation equations are distributed over the volume encompassing the particle size, as opposed to the Dirac delta function generally used in the point-particle approach.The proposed approach is benchmarked against three different flow configurations in a numerical framework based on large eddy simulation（LES） turbulence closure.First, the flow over a circular cylinder is simulated for a Reynolds number of 3900 at 1 atm pressure.Results show good agreement with experimental data for the mean streamwise velocity and the vortex shedding frequency in the wake region.The calculated flowfield exhibits correct physics, which the conventional point-particle approach fails to capture.The second case deals with diesel jet injection in quiescent environment over a pressure range of 1.1–5.0 MPa.The calculated jet penetration depth closely matches measurements.It decreases with increasing chamber pressure, due to enhanced drag force in a denser fluid environment.Finally, water and acetone jet injection normal to air crossflow is studied at1 atm.The calculated jet penetration and Sauter mean diameter of liquid droplets compare very well with measurements.
基金Project supported by the National Natural Science Foundation of China (Grant No 10875100)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61572529,61871407,and 61801522)the China Postdoctoral Science Foundation(Grant Nos.2013M542119 and 2014T70772)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Nos.11490551,11772172,11702158)。
文摘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.
基金supported by the European Research Council Grant No.ERC-2013-CoG-616186,TRITOSthe Swedish Research Council(VR)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Nos.91752117,11632016,and 11372275)the Natural Science Foundation of Zhejiang Province of China(No.LY17A020005)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11121403 and 11504384
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61379153 and 61572529)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos.12304340,12074241,11929401,and 52130204)the Science and Technology Commission of Shanghai Municipality (Grant Nos.20501130600,21JC1402600,and 21JC1402700)+2 种基金the Shanghai Pujiang Program (Grant No.23PJ1403200)the Key Research Project of Zhejiang Laboratory (Grant No.2021PE0AC02)the startup funding of the Chinese University of Hong Kong,Shenzhen (Grant No.UDF01002563)。
文摘While non-Hermiticity provokes intriguing phenomena without Hermitian counterparts, e.g., the skin effect and the breakdown of bulk-boundary correspondence, attracting extensive attention both in fundamental physics and device engineering, the role of finite sizes therein remains elusive. Here, we propose a class of finite-size-induced non-Hermitian phase transitions, relying upon higher-order topological invariants associated with real-space wave functions. The phase diagrams for general non-Hermitian chiral models are further acquired to demonstrate our topological definition. Such phase transitions are elucidated qualitatively by an effective intercell coupling alteration that depends on finite sizes in respective directions. Besides, we mimic these phenomena by analogizing the circuit Laplacian in finite-size electric circuits with nonreciprocal couplings. The resultant admittance spectra agree with our theoretical predictions. Our findings shed light on the finite-size mechanism of non-Hermitian topological phase transitions and pave the way for applications in switching and sensing.
基金This work was supported by the National Basic Research "973" Project in China the National Natural Science Foundation in China (Grant Nos. 59876039, 59936140 and 39970621).
文摘The influences of finite-size effects on the self-organized criticality (SOC) of the traditional forest-fire model are investigated by means of a new method. The forest size is originally set to a value much greater than the correla-tion length of the forest. Finite-size effects are then studied by equally dividing the forest into more and more separate subsystems on condition that the forest size, igniting prob-ability and planting probability are invariant. A new phe-nomenon, i.e. the finite-size effects with one-side frequency peak, is observed. The boundary between two neighboring subsystems can be regarded as a firebreak. The concept of ’separation ability’ is introduced to represent the probability for the firebreak to block off the fire successfully. Restrain-ing effects of separation ability on finite-size effects are ana-lyzed. Finite-size effects and separation ability, as well as their relations are found to have practical importance to the actual forest-fire protection.
基金supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019)received a postdoctoral fellowship funded by the KunmingUniversity of Science and Technology
文摘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.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFA1405400)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301902),the National Natural Science Foundation of China(Grant No.12274290)the sponsor-ship from Yangyang Development Fund.
文摘We perform a comprehensive study of the electron-doped t-t′-J model on cylinders with density matrix renormalization group(DMRG).We conduct a systematic study on the finite-size and boundary condition effects on t-t′-J model on cylinders.Periodic and anti-periodic boundary conditions are implemented along the circumference direction,with the system’s width extending up to as large as 8 lattice units.We study doping levels of 1/6,1/8,and 1/12,which represent the most interesting region in the phase diagram of electron-doped cuprates.We find that for width-4 and width-6 systems,the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and system widths,indicating the presence of large finite size effect in the t-t′-J model.We also have a careful analysis of the d-wave pairing correlations which also change quantitatively with boundary conditions and widths of the system.However,the pairing correlations are enhanced when the system becomes wider for all dopings,suggesting the existence of possible long-range superconducting order in the thermodynamic limit.The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach.For the width-8 system,only Neel(stripe)state can be stabilized in DMRG calculation for 1/12(1/6)doping,while both stripe and Neel states are stable in the DMRG sweep for 1/8 doping,regardless of the boundary conditions.These results indicate that 1/8 doping is likely to lie on the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping,consistent with the previous study.The sensitivity of the ground state on boundary conditions and size observed for narrow systems is similar to that found in the t′-Hubbard model,where the t′term introduces frustration and makes the stripe state fragile.The study of different boundary conditions provides a useful tool to check the finite size effect in the future DMRG calculations.
基金supported by the National Natural Science Foundation of China(No.12305143)the China Postdoctoral Science Foundation(No.2023M731467).
文摘The sign of higher-order multiplicity fluctuations is a very important parameter for exploring QCD phase transitions.The kurtosis of the net-baryon is typically negative in simulations of the dynamics of the conserved net-baryon density near the QCD critical point.This paper considers the effects of finite size on multiplicity fluctuations with equilibrium critical fluctuations.It is found that the multiplicity fluctuations(or the magnitude of the correlation function D_(ij))are dramatically suppressed with decreasing system size when the size of the system is small compared with the correlation length,which is the so-called acceptance dependence.Consequently,the small correlation function of the small system size results in the magnitude of the negative contribution(~D_(ij)^(4))in the four-point correlation function dominating the positive term(~D_(ij)^(5)),and this finite-size effect induces a dip structure near the QCD critical point.
基金Project supported by the National Natural Science Foundation of China(Grant No.11172319)the Scientific Fund of Chinese Universities(Grant Nos.2011JS046 and 2013BH008)+1 种基金the Opening Fund of State Key Laboratory of Nonlinear Mechanics,Program for New Century Excellent Talents in University,China(Grant No.NCET-13-0552)the National Science Foundation for Post-doctoral Scientists of China(Grant No.2013M541086)
文摘Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.
基金financially supported by the National Natural Science Foundation of China (Grants 51878152 and 51461135001)the Ministry of Science and Technology of China "973 Project" (Grant 2015CB655102)
文摘The pore configuration in porous medium is assumed to be the randomly distributed cube-like particles which can overlap each other in the periodic cubic domain, and the impact of particle characteristics on the percolation property of these cube-like particle packing systems is analyzed.Firstly, by combining the percolation models and finite-size scaling analysis, three numerical parameters(i.e., percolation transition width △L, local percolation threshold ψ_c(L), and correlation length exponent v) for the cube-like particle systems with shape parameter s in[1.0, +∞] are derived successively. Then, based on the relation between the percolation thresholdψ_c in infinite space and the local percolation threshold ψ_c(L), the corresponding ψ_c with s in[1.0, +∞] are further determined. It is shown from the study that the characteristics of cube-like particles have significant influence on the global percolation threshold ψ_c of the particle packing systems. As the parameter s increases from 1.0 to +∞, the percolation threshold ψ_c will go down persistently. When the surface of cube-like particles is cubical and spherical, respectively, the minimum and maximum thresholds ψ_c,min and ψ_c,max are obtained.
文摘A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.
基金Project supported by the National Natural Science Foundation of China (Grants Nos. 11174359 and 10874232)the National Basic Research Program of China (Grant No. 2012CB932302)
文摘In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J0 J1 J2 model, which corresponds to the staggered j-j′ model on a square lattice and a honeycomb lattice when J1/J0 equals 1 and O, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J1/J0 changing from 0 to 1 as a function of coupling ratio a = J2/J0. We extract all the critical values of the coupling ratio ac for these models, and we also obtain the critical exponents v,β/ν, and η using different finite-size scaling ansatz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum ciriteial points in these models.
基金Project supported by the Botswana International University of Science and Technology Research Initiation(Grant Nos.R00015 and S00100)。
文摘We present a three-party reference frame independent quantum key distribution protocol which can be implemented without any alignment of reference frames between the sender and the receiver.The protocol exploits entangled states to establish a secret key among three communicating parties.We derive the asymptotic key rate for the proposed protocol against collective attacks and perform a finite-size key security analysis against general attacks in the presence of statistical fluctuations.We investigate the impact of reference frame misalignment on the stability of our protocol,and we obtain a transmission distance of 180 km,200 km,and 230 km for rotation of reference framesβ=π/6,β=π/8 andβ=0,respectively.Remarkably,our results demonstrate that our proposed protocol is not heavily affected by an increase in misalignment of reference frames as the achievable transmission distances are still comparable to the case where there is no misalignment in reference frames(whenβ=0).We also simulate the performance of our protocol for a fixed number of signals.Our results demonstrate that the protocol can achieve an effective key generation rate over a transmission distance of about 120 km with realistic 107 finite data signals and approximately achieve 195 km with 109 signals.Moreover,our proposed protocol is robust against noise in the quantum channel and achieves a threshold error rate of 22.7%.
基金National Natural Science Foundation of China under Grant Nos.10675048,50872038,and 10604017
文摘Through using the methods of finite-size effect and short time dynamic scaling,we study the criticalbehavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment.Throughcomprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition fromdisease-free state to endemic state with a finite population density.We determine the critical population density,abovewhich the system reaches an epidemic spreading stationary state.We also perform a scaling analysis to determine theorder parameter and critical relaxation exponents.The results show that the model does not belong to the usual directedpercolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.
基金the National Key Basic Research Program of China(Grant No.2022YFA1404800)the National Natural Science Foundation of China(Grant Nos.12234007 and 12221004)supported by Science and Technology Commission of Shanghai Municipality,China(Grant Nos.19XD1434600,2019SHZDZX01,19DZ2253000,20501110500,and 21DZ1101500)。
文摘Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.
