Activation pruning reduces neural network complexity by eliminating low-importance neuron activations,yet identifying the critical pruning threshold—beyond which accuracy rapidly deteriorates—remains computationally...Activation pruning reduces neural network complexity by eliminating low-importance neuron activations,yet identifying the critical pruning threshold—beyond which accuracy rapidly deteriorates—remains computationally expensive and typically requires exhaustive search.We introduce a thermodynamics-inspired framework that treats activation distributions as energy-filtered physical systems and employs the free energy of activations as a principled evaluation metric.Phase-transition-like phenomena in the free-energy profile—such as extrema,inflection points,and curvature changes—yield reliable estimates of the critical pruning threshold,providing a theoretically grounded means of predicting sharp accuracy degradation.To further enhance efficiency,we propose a renormalized free energy technique that approximates full-evaluation free energy using only the activation distribution of the unpruned network.This eliminates repeated forward passes,dramatically reducing computational overhead and achieving speedups of up to 550×for MLPs.Extensive experiments across diverse vision architectures(MLP,CNN,ResNet,MobileNet,Vision Transformer)and text models(LSTM,BERT,ELECTRA,T5,GPT-2)on multiple datasets validate the generality,robustness,and computational efficiency of our approach.Overall,this work establishes a theoretically grounded and practically effective framework for activation pruning,bridging the gap between analytical understanding and efficient deployment of sparse neural networks.展开更多
In a superconductor embedded with a quantum magnetic impurity,the Kondo effect is involved,leading to the competition between the Kondo singlet phase and the superconductivity phase.By means of the natural orbitals re...In a superconductor embedded with a quantum magnetic impurity,the Kondo effect is involved,leading to the competition between the Kondo singlet phase and the superconductivity phase.By means of the natural orbitals renormalization group(NORG)method,we revisit the problem of a quantum magnetic impurity coupled with a conventional s-wave superconductor.Here we present a detailed study focusing on the impurity spin polarization and susceptibility,the Kondo screening cloud,as well as the number and structures of the active natural orbitals(ANOs).In the superconducting phase,the impurity spin is partially polarized,indicating that the impurity remains partially screened by the quantum fluctuations.Furthermore,the impurity spin susceptibility becomes divergent,resulting from the presence of residual local moment formed at the impurity site.Correspondingly,a non-integral(incomplete)Kondo cloud is formed,although the ground state is a spin doublet in this phase.In comparison,the Kondo cloud is complete in the Kondo singlet phase as expected.We also quantify the critical point,where the quantum phase transition from a Kondo singlet phase to a superconducting phase occurs,which is consistent with that in previous works.On the other hand,it is illustrated that only one ANO emerges in both quantum phases.The structures of the ANO,projected into both the real space and momentum space,are distinct in the Kondo singlet phase from that in the superconducting phase.More specifically,in the Kondo singlet phase,the ANO keeps fully active with half-occupied,and the superconducting gap has negligible influence on its structure.On the contrary,in the superconducting phase,the ANO tends to be inactive and its structure changes significantly as the superconducting gap increases.Additionally,our investigation demonstrates that the NORG method is reliable and convenient to solve the quantum impurity problems in superconductors as well,which will promote further theoretical studies on the Kondo problems in such systems using numerical methods.展开更多
We investigate the behavior of non-Hermitian birefringent Dirac fermions by examining their interaction with electromagnetic fields through renormalization group analysis. Our research reveals that the interplay betwe...We investigate the behavior of non-Hermitian birefringent Dirac fermions by examining their interaction with electromagnetic fields through renormalization group analysis. Our research reveals that the interplay between non-Hermiticity and birefringence leads to distinct behaviors in two and three dimensions, where the system exhibits different fixed points and scaling properties due to dimension-dependent charge renormalization effects. In two dimensions, where the electronic charge remains unrenormalized, the system flows in the deep infrared limit from non-Hermitian birefringent spin-3/2fermions to two copies of non-Hermitian spin-1/2 Dirac fermions, demonstrating a crossover of relativistic liquid and nonrelativistic liquid. In three dimensions, dynamic screening of electromagnetic interactions modifies the logarithmic growth of Fermi velocity, leading to richer quantum corrections while maintaining similar suppression of birefringence in the infrared limit. Our findings provide theoretical insights into the emergence of Lorentz symmetry in non-Hermitian systems,laying theoretical foundations for studying low-energy behavior in other non-Hermitian models.展开更多
The system consisting of(2+1)-dimensional quasirelativistic birefringent Dirac fermions with Coulomb interactions and retarded current–current interactions is described by a quantum field theory similar to reduced qu...The system consisting of(2+1)-dimensional quasirelativistic birefringent Dirac fermions with Coulomb interactions and retarded current–current interactions is described by a quantum field theory similar to reduced quantum electrodynamics.We used the perturbative renormalization group method to study the low-energy behavior of the system and found that it flows to a fixed point of the non-Fermi liquid composed of relativistic pseudospin-1/2 Dirac fermions in the deep infrared limit.At the fixed point,the fermion Green function exhibits a finite anomalous dimension,and the residue of the quasiparticle pole vanishes in a power-law fashion.Our research provides new theoretical perspectives for understanding the origin of spin-1/2 fermions in the standard model.展开更多
A direct renormalization method without spectrum theory is proposed to compute the perturbation of solitons in nearly integrable systems with multiple small parameters.The evolution equations of these parameters in un...A direct renormalization method without spectrum theory is proposed to compute the perturbation of solitons in nearly integrable systems with multiple small parameters.The evolution equations of these parameters in unperturbed solitons are obtained as the renormalization equations.Compared with routine methods,the advantages of the renormalization method are that the formulation is only based on a clear and simple mathematical theory,namely the Taylor expansion at a general point,the secular terms in perturbation series are eliminated automatically,any priori physical assumption on the form of the solution is avoided,multiple time scales arise naturally from the final naive perturbation expansion,and the Green’s function and corresponding spectrum of linear differential operators are not needed.As applications,the perturbation of solitons for KDV,MKdV and nonlinear Schrodinger equations,are obtained.展开更多
Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity.Here we extend the method to treat periodic ...Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity.Here we extend the method to treat periodic orbits or limit cycles.Interesting normal forms could be derived through a generalization of the concept'resonance',which offers nontrivial analytic approximations.Compared with traditional techniques such as multi-scale methods,the current scheme proceeds in a very straightforward and simple way,delivering not only the period and the amplitude but also the transient path to limit cycles.The method is demonstrated with several examples including the Duffing oscillator,van der Pol equation and Lorenz equation.The obtained solutions match well with numerical results and with those derived by traditional analytic methods.展开更多
Generally,referring to the stability of perovskite,the most studied perovskite material has been MA-free mixed-cationperovskite.The precise role of MA in the light-thermal-humid stability of perovskite solar cells sti...Generally,referring to the stability of perovskite,the most studied perovskite material has been MA-free mixed-cationperovskite.The precise role of MA in the light-thermal-humid stability of perovskite solar cells still lacks ofa systematically understanding.In this work,the evolution of crystallographic structures,intermediate phase,ultrafast dynamics,and thermal decomposition behavior of MA-mixed perovskite FA_(1-x)MA_(x)PbI_(3)(x=0–100%)areinvestigated.The influence of MA on the stability of devices under heat,light,and humidity exposure arerevealed.In the investigated compositional space(x=0–100%),device efficiencies vary from 19.5%to 22.8%,andthe light,thermal,and humidity exposure stability of the related devices are obviously improved forFA1-xMAxPbI_(3)(x=20%–30%).Incorporation 20%–30%of MA cations lowers nucleation barrier and causes asignificant volume shrinkage,which enhances the interaction between FA and I,thus improving crystallizationand stability of the FA_(1-x)MA_(x)PbI_(3).Thermal behavior analysis reveals that the decomposition temperature of FA_(0.8)MA_(0.2)PbI_(3)reaches 247℃(FAPbI_(3),233℃)and trace amounts of MA cations enhance the thermal stability ofthe perovskite.Remarkably,we observe lattice shrinkage using spherical aberration corrected transmissionelectron microscope(AC-TEM).This work implies that stabilizing perovskites will be realized by incorporatingtrace amounts of MA,which improve the crystallization and carrier transport,leading to improved stability andperformances.展开更多
Accurate evaluation of elec-tron correlations is essential for the reliable quantitative de-scription of electronic struc-tures in strongly correlated sys-tems,including bond-dissociat-ing molecules,polyradicals,large...Accurate evaluation of elec-tron correlations is essential for the reliable quantitative de-scription of electronic struc-tures in strongly correlated sys-tems,including bond-dissociat-ing molecules,polyradicals,large conjugated molecules,and transition metal complex-es.To provide a user-friendly tool for studying such challeng-ing systems,our team developed Kylin 1.0[J.Comput.Chem.44,1316(2023)],an ab initio quantum chemistry program designed for efficient density matrix renormalization group(DMRG)and post-DMRG methods,enabling high-accuracy calculations with large active spaces.We have now further advanced the software with the release of Kylin 1.3,featuring optimized DMRG algorithms and an improved tensor contraction scheme in the diagonaliza-tion step.Benchmark calculations on the Mn_(4)CaO_(5)cluster demonstrate a remarkable speed-up of up to 16 fater than Kylin 1.0.Moreover,a more user-friendly and efficient algorithm[J.Chem.Theory Comput.17,3414(2021)]for sampling configurations from DMRG wavefunc-tion is implemented as well.Additionally,we have also implemented a spin-adapted version of the externally contracted multi-reference configuration interaction(EC-MRCI)method[J.Phys.Chem.A 128,958(2024)],further enhancing the program’s efficiency and accuracy for electron correlation calculations.展开更多
We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in l...We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory(LEFT).The on-shell method significantly simplifies the construction of scattering amplitudes.By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals,we bypass the need for direct loop integral calculations.The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients,which will aid in precision experimental fitting of these coefficients.展开更多
A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most s...A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most salient feature of the current approach is that only linear algebraic equations need to be solved to implement the resummation for closed-form exact solution and parameter dependence,which does not require any sophisticated analysis like Cole-Hopf transformation or Painlevétest.New exact solutions of typical NPDEs are computed with this novel method,including one-and two-soliton(solitary wave)solutions,periodic solutions of exponential or elliptic function type.Moreover,exact reduced equations may also be conveniently computed for further analysis.展开更多
High multipole electromagnetic transitions are rare in nature.The highest-multipole transition observed in atomic nuclei is the electric hexacontatetrapole E6 transition from the T_(1/2)=2.54(2)-min J^(π)=1_(9/2)-iso...High multipole electromagnetic transitions are rare in nature.The highest-multipole transition observed in atomic nuclei is the electric hexacontatetrapole E6 transition from the T_(1/2)=2.54(2)-min J^(π)=1_(9/2)-isomer to the 7/2^(-)ground state in^(53)Fe with an angular momentum change of six units.In the present work,we performed ab initio calculations for this unique case by employing chiral effective field theory(EFT)forces.The in-medium similarity renormalization group is used to derive the valence-space effective Hamiltonian and multipolar transition operators.Bare nucleon charges were used in all the multipolar transition rate calculations,providing good agreement with the experimental data.The valence space takes the full fp shell.In^(53)Fe,the low-lying states were dominated by the 0f_(7/2)component.Two different versions of the chiral EFT two-plus three-nucleon interaction were used to test the dependence on the interaction used.We also tested the convergence of the transition rate calculations against the harmonic oscillator parameter hΩand basis truncations e_(max)and E_(3max)for twoand three-nucleon forces,respectively.展开更多
We are studying the motion of a random walker in generalised d-dimensional continuum with unit step length (up to 10 dimensions) and its projected one dimensional motion numerically. The motion of a random walker in l...We are studying the motion of a random walker in generalised d-dimensional continuum with unit step length (up to 10 dimensions) and its projected one dimensional motion numerically. The motion of a random walker in lattice or continuum is well studied in statistical physics but what will be the statistics of projected one dimensional motion of higher dimensional random walker is yet to be explored. Here in this paper, by addressing this particular type of problem, it shows that the projected motion is diffusive irrespective of any dimension;however, the diffusion rate is changing inversely with dimensions. As a consequence, it can be predicted that for the one dimensional projected motion of infinite dimensional random walk, the diffusion rate will be zero. This is an interesting result, at least pedagogically, which implies that though in infinite dimensions there is diffusion, its one dimensional projection is motionless. At the end of the discussion we are able to make a good comparison between projected one dimensional motion of generalised d-dimensional random walk with unit step length and pure one dimensional random walk with random step length varying uniformly between -h to h where h is a “step length renormalizing factor”.展开更多
Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are o...Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.展开更多
During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstru...During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.展开更多
The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two c...The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two cases are simulated and compared with the experimental data. It shows that the RNG turbulence model can give an appropriate prediction for the configuration of equilibrium scour hole, and it is applicable to this situation. The local scour mechanism around submarine pipelines including the flow structure, shear stress distribution and pressure field is then analyzed and compared with experiments. For further comparison and validation, especially for the flow structure, a numerical calculation employing the large eddy simulation （LES） is also conducted. The numerical results of RNG demonstrate that the critical factor governing the equilibrium profile is the seabed shear stress distribution in the case of bed load sediment transport, and the two-equation RNG turbulence model coupled with the law of wall is capable of giving a satisfying estimation for the bed shear stress. Moreover, the piping phenomena due to the great difference of pressure between the upstream and downstream parts of pipelines and the vortex structure around submarine pipelines are also simulated successfully, which are believed to be the important factor that lead to the onset of local scour.展开更多
Stochastic dynamic analysis of the nonlinear system is an open research question which has drawn many scholars'attention for its importance and challenge.Fokker–Planck–Kolmogorov(FPK)equation is of great signifi...Stochastic dynamic analysis of the nonlinear system is an open research question which has drawn many scholars'attention for its importance and challenge.Fokker–Planck–Kolmogorov(FPK)equation is of great significance because of its theoretical strictness and computational accuracy.However,practical difficulties with the FPK method appear when the analysis of multi-degree-offreedom(MDOF)with more general nonlinearity is required.In the present paper,by invoking the idea of equivalence of probability flux,the general high-dimensional FPK equation related to MDOF system is reduced to one-dimensional FPK equation.Then a cell renormalized method(CRM)which is based on the numerical reconstruction of the derived moments of FPK equation is introduced by coarsening the continuous state space into a discretized region of cells.Then the cell renormalized FPK(CR-FPK)equation is solved by difference method.Three numerical examples are illustrated and the effectiveness of proposed method is assessed and verified.展开更多
The fragmentation test of granite subjected to strain rate of 10~010~2s~ -1 was carried out using split Hopkinson pressure bar(SHPB) whose diameter is 75 mm, where half-sine loading waveform was performed. The sieving...The fragmentation test of granite subjected to strain rate of 10~010~2s~ -1 was carried out using split Hopkinson pressure bar(SHPB) whose diameter is 75 mm, where half-sine loading waveform was performed. The sieving statistics results of the fragments show that the distribution of the fragments is a fractal, and the fractal dimension values fall into the range of 1.22.4. The correlation analysis between the fractal dimension and the logarithm of the energy density shows that they have approximately linear relation. Finally, based on damage theory and scale invariant principle, the fragmentation model with renormalization method was put forward, and the fractal dimension value predicted with the model was compared with the test results. It is found that the fractal dimension value obtained from the improved fragmentation model is more reasonable.展开更多
In this paper,we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group(fRG)approach.The f RG is a nonperturbative continuum field appr...In this paper,we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group(fRG)approach.The f RG is a nonperturbative continuum field approach,in which quantum,thermal and density fluctuations are integrated successively with the evolution of the renormalization group(RG)scale.The f RG results for the QCD phase structure and the location of the critical end point(CEP),the QCD equation of state(EoS),the magnetic EoS,baryon number fluctuations confronted with recent experimental measurements,various critical exponents,spectral functions in the critical region,the dynamical critical exponent,etc,are presented.Recent estimates of the location of the CEP from first-principle QCD calculations within f RG and Dyson-Schwinger equations,which pass through lattice benchmark tests at small baryon chemical potentials,converge in a rather small region at baryon chemical potentials of about 600 MeV.A region of inhomogeneous instability indicated by a negative wave function renormalization is found withμ_(B)■420 MeV.It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments could arise from the increasingly sharp crossover in the regime of low collision energy.展开更多
Adopted the fractal tree-like failure model, and established the renormalization group transform function of fractured fault, and investigated the mechanism of water-inrush from fault, and found out the critical proba...Adopted the fractal tree-like failure model, and established the renormalization group transform function of fractured fault, and investigated the mechanism of water-inrush from fault, and found out the critical probability of water-inrush from fault caused by fault fracture. The results indicate： when the failure rate P is less than the critical failure rate Pc=0.206 3, the failure of the system is just partial. When P is more than the critical failure rate Pc=0.206 3, the random distributed crannies concentrate to certain domain of attraction （such as the maximum shear stress face in the fault） gradually. The process will continue until the crannies run-through, forming conductivity channel, and cause water-inrush from fault.展开更多
基金output of a research project implemented as part of the Basic Research Program at HSE University。
文摘Activation pruning reduces neural network complexity by eliminating low-importance neuron activations,yet identifying the critical pruning threshold—beyond which accuracy rapidly deteriorates—remains computationally expensive and typically requires exhaustive search.We introduce a thermodynamics-inspired framework that treats activation distributions as energy-filtered physical systems and employs the free energy of activations as a principled evaluation metric.Phase-transition-like phenomena in the free-energy profile—such as extrema,inflection points,and curvature changes—yield reliable estimates of the critical pruning threshold,providing a theoretically grounded means of predicting sharp accuracy degradation.To further enhance efficiency,we propose a renormalized free energy technique that approximates full-evaluation free energy using only the activation distribution of the unpruned network.This eliminates repeated forward passes,dramatically reducing computational overhead and achieving speedups of up to 550×for MLPs.Extensive experiments across diverse vision architectures(MLP,CNN,ResNet,MobileNet,Vision Transformer)and text models(LSTM,BERT,ELECTRA,T5,GPT-2)on multiple datasets validate the generality,robustness,and computational efficiency of our approach.Overall,this work establishes a theoretically grounded and practically effective framework for activation pruning,bridging the gap between analytical understanding and efficient deployment of sparse neural networks.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12104247 and 11934020)。
文摘In a superconductor embedded with a quantum magnetic impurity,the Kondo effect is involved,leading to the competition between the Kondo singlet phase and the superconductivity phase.By means of the natural orbitals renormalization group(NORG)method,we revisit the problem of a quantum magnetic impurity coupled with a conventional s-wave superconductor.Here we present a detailed study focusing on the impurity spin polarization and susceptibility,the Kondo screening cloud,as well as the number and structures of the active natural orbitals(ANOs).In the superconducting phase,the impurity spin is partially polarized,indicating that the impurity remains partially screened by the quantum fluctuations.Furthermore,the impurity spin susceptibility becomes divergent,resulting from the presence of residual local moment formed at the impurity site.Correspondingly,a non-integral(incomplete)Kondo cloud is formed,although the ground state is a spin doublet in this phase.In comparison,the Kondo cloud is complete in the Kondo singlet phase as expected.We also quantify the critical point,where the quantum phase transition from a Kondo singlet phase to a superconducting phase occurs,which is consistent with that in previous works.On the other hand,it is illustrated that only one ANO emerges in both quantum phases.The structures of the ANO,projected into both the real space and momentum space,are distinct in the Kondo singlet phase from that in the superconducting phase.More specifically,in the Kondo singlet phase,the ANO keeps fully active with half-occupied,and the superconducting gap has negligible influence on its structure.On the contrary,in the superconducting phase,the ANO tends to be inactive and its structure changes significantly as the superconducting gap increases.Additionally,our investigation demonstrates that the NORG method is reliable and convenient to solve the quantum impurity problems in superconductors as well,which will promote further theoretical studies on the Kondo problems in such systems using numerical methods.
基金Project supported by the National Key Research and Development Program of China (Grants Nos. 2021YFA1400900,2021YFA0718300, and 2021YFA1400243)the National Natural Science Foundation of China (Grant Nos. 61835013,12174461, and 12234012)the Fund from the Space Application System of China Manned Space Program。
文摘We investigate the behavior of non-Hermitian birefringent Dirac fermions by examining their interaction with electromagnetic fields through renormalization group analysis. Our research reveals that the interplay between non-Hermiticity and birefringence leads to distinct behaviors in two and three dimensions, where the system exhibits different fixed points and scaling properties due to dimension-dependent charge renormalization effects. In two dimensions, where the electronic charge remains unrenormalized, the system flows in the deep infrared limit from non-Hermitian birefringent spin-3/2fermions to two copies of non-Hermitian spin-1/2 Dirac fermions, demonstrating a crossover of relativistic liquid and nonrelativistic liquid. In three dimensions, dynamic screening of electromagnetic interactions modifies the logarithmic growth of Fermi velocity, leading to richer quantum corrections while maintaining similar suppression of birefringence in the infrared limit. Our findings provide theoretical insights into the emergence of Lorentz symmetry in non-Hermitian systems,laying theoretical foundations for studying low-energy behavior in other non-Hermitian models.
基金supported by the National Key Research and Development Program of China(Grant Nos.2021YFA1400900,2021YFA0718300,and 2021YFA1400243)the National Natural Science Foundation of China(Grant Nos.61835013,12174461,and 12234012)Space Application System of China Manned Space Program.
文摘The system consisting of(2+1)-dimensional quasirelativistic birefringent Dirac fermions with Coulomb interactions and retarded current–current interactions is described by a quantum field theory similar to reduced quantum electrodynamics.We used the perturbative renormalization group method to study the low-energy behavior of the system and found that it flows to a fixed point of the non-Fermi liquid composed of relativistic pseudospin-1/2 Dirac fermions in the deep infrared limit.At the fixed point,the fermion Green function exhibits a finite anomalous dimension,and the residue of the quasiparticle pole vanishes in a power-law fashion.Our research provides new theoretical perspectives for understanding the origin of spin-1/2 fermions in the standard model.
基金supported by the Special Program for Ability Promotion of the Basic and Scientific Research(Grant No.2023JCYJ-01).
文摘A direct renormalization method without spectrum theory is proposed to compute the perturbation of solitons in nearly integrable systems with multiple small parameters.The evolution equations of these parameters in unperturbed solitons are obtained as the renormalization equations.Compared with routine methods,the advantages of the renormalization method are that the formulation is only based on a clear and simple mathematical theory,namely the Taylor expansion at a general point,the secular terms in perturbation series are eliminated automatically,any priori physical assumption on the form of the solution is avoided,multiple time scales arise naturally from the final naive perturbation expansion,and the Green’s function and corresponding spectrum of linear differential operators are not needed.As applications,the perturbation of solitons for KDV,MKdV and nonlinear Schrodinger equations,are obtained.
文摘Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity.Here we extend the method to treat periodic orbits or limit cycles.Interesting normal forms could be derived through a generalization of the concept'resonance',which offers nontrivial analytic approximations.Compared with traditional techniques such as multi-scale methods,the current scheme proceeds in a very straightforward and simple way,delivering not only the period and the amplitude but also the transient path to limit cycles.The method is demonstrated with several examples including the Duffing oscillator,van der Pol equation and Lorenz equation.The obtained solutions match well with numerical results and with those derived by traditional analytic methods.
基金supported by the Nation Key R&D Program of China(Grant Numbers:2023YFC3906103)the Natural Science Foundation of Hunan Province(No.2022JJ30757)+1 种基金Entrepreneurship Research Team Project(No.1053320220430)Guangdong Science and Technology Planning Project(2018B030323010).
文摘Generally,referring to the stability of perovskite,the most studied perovskite material has been MA-free mixed-cationperovskite.The precise role of MA in the light-thermal-humid stability of perovskite solar cells still lacks ofa systematically understanding.In this work,the evolution of crystallographic structures,intermediate phase,ultrafast dynamics,and thermal decomposition behavior of MA-mixed perovskite FA_(1-x)MA_(x)PbI_(3)(x=0–100%)areinvestigated.The influence of MA on the stability of devices under heat,light,and humidity exposure arerevealed.In the investigated compositional space(x=0–100%),device efficiencies vary from 19.5%to 22.8%,andthe light,thermal,and humidity exposure stability of the related devices are obviously improved forFA1-xMAxPbI_(3)(x=20%–30%).Incorporation 20%–30%of MA cations lowers nucleation barrier and causes asignificant volume shrinkage,which enhances the interaction between FA and I,thus improving crystallizationand stability of the FA_(1-x)MA_(x)PbI_(3).Thermal behavior analysis reveals that the decomposition temperature of FA_(0.8)MA_(0.2)PbI_(3)reaches 247℃(FAPbI_(3),233℃)and trace amounts of MA cations enhance the thermal stability ofthe perovskite.Remarkably,we observe lattice shrinkage using spherical aberration corrected transmissionelectron microscope(AC-TEM).This work implies that stabilizing perovskites will be realized by incorporatingtrace amounts of MA,which improve the crystallization and carrier transport,leading to improved stability andperformances.
基金supported by Shandong Provincial Nat-ural Science Foundation(ZR2024ZD30)the National Natural Science Foundation of China(Nos.22325302 and 22403100).
文摘Accurate evaluation of elec-tron correlations is essential for the reliable quantitative de-scription of electronic struc-tures in strongly correlated sys-tems,including bond-dissociat-ing molecules,polyradicals,large conjugated molecules,and transition metal complex-es.To provide a user-friendly tool for studying such challeng-ing systems,our team developed Kylin 1.0[J.Comput.Chem.44,1316(2023)],an ab initio quantum chemistry program designed for efficient density matrix renormalization group(DMRG)and post-DMRG methods,enabling high-accuracy calculations with large active spaces.We have now further advanced the software with the release of Kylin 1.3,featuring optimized DMRG algorithms and an improved tensor contraction scheme in the diagonaliza-tion step.Benchmark calculations on the Mn_(4)CaO_(5)cluster demonstrate a remarkable speed-up of up to 16 fater than Kylin 1.0.Moreover,a more user-friendly and efficient algorithm[J.Chem.Theory Comput.17,3414(2021)]for sampling configurations from DMRG wavefunc-tion is implemented as well.Additionally,we have also implemented a spin-adapted version of the externally contracted multi-reference configuration interaction(EC-MRCI)method[J.Phys.Chem.A 128,958(2024)],further enhancing the program’s efficiency and accuracy for electron correlation calculations.
基金supported by the National Science Foundation of China under Grants Nos.12347145,12347105,12375099,and 12047503the National Key Research and Development Program of China Grant Nos.2020YFC2201501 and 2021YFA0718304。
文摘We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory(LEFT).The on-shell method significantly simplifies the construction of scattering amplitudes.By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals,we bypass the need for direct loop integral calculations.The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients,which will aid in precision experimental fitting of these coefficients.
基金supported by the National Natural Science Foundation of China under Grant No.12375030the National Natural Science Foundation of China under Grant No.12471084.
文摘A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations(NPDEs)based on a series expansions of solutions and a renormalization group(RG)related resummation.The most salient feature of the current approach is that only linear algebraic equations need to be solved to implement the resummation for closed-form exact solution and parameter dependence,which does not require any sophisticated analysis like Cole-Hopf transformation or Painlevétest.New exact solutions of typical NPDEs are computed with this novel method,including one-and two-soliton(solitary wave)solutions,periodic solutions of exponential or elliptic function type.Moreover,exact reduced equations may also be conveniently computed for further analysis.
基金supported by the National Key R&D Program of China(Nos.2024YFA1610900 and 2023YFA1606401)the National Natural Science Foundation of China(Nos.12335007 and 12035001)the United Kingdom Science and Technology Facilities Council(No.ST/V001108/1)。
文摘High multipole electromagnetic transitions are rare in nature.The highest-multipole transition observed in atomic nuclei is the electric hexacontatetrapole E6 transition from the T_(1/2)=2.54(2)-min J^(π)=1_(9/2)-isomer to the 7/2^(-)ground state in^(53)Fe with an angular momentum change of six units.In the present work,we performed ab initio calculations for this unique case by employing chiral effective field theory(EFT)forces.The in-medium similarity renormalization group is used to derive the valence-space effective Hamiltonian and multipolar transition operators.Bare nucleon charges were used in all the multipolar transition rate calculations,providing good agreement with the experimental data.The valence space takes the full fp shell.In^(53)Fe,the low-lying states were dominated by the 0f_(7/2)component.Two different versions of the chiral EFT two-plus three-nucleon interaction were used to test the dependence on the interaction used.We also tested the convergence of the transition rate calculations against the harmonic oscillator parameter hΩand basis truncations e_(max)and E_(3max)for twoand three-nucleon forces,respectively.
文摘We are studying the motion of a random walker in generalised d-dimensional continuum with unit step length (up to 10 dimensions) and its projected one dimensional motion numerically. The motion of a random walker in lattice or continuum is well studied in statistical physics but what will be the statistics of projected one dimensional motion of higher dimensional random walker is yet to be explored. Here in this paper, by addressing this particular type of problem, it shows that the projected motion is diffusive irrespective of any dimension;however, the diffusion rate is changing inversely with dimensions. As a consequence, it can be predicted that for the one dimensional projected motion of infinite dimensional random walk, the diffusion rate will be zero. This is an interesting result, at least pedagogically, which implies that though in infinite dimensions there is diffusion, its one dimensional projection is motionless. At the end of the discussion we are able to make a good comparison between projected one dimensional motion of generalised d-dimensional random walk with unit step length and pure one dimensional random walk with random step length varying uniformly between -h to h where h is a “step length renormalizing factor”.
基金This work was supported by the National Natural Science Foundation of China (No. 40274044).
文摘Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.
基金the National Natural Science Foundation of China(Grant No.51534002)the Special Funds for Technological Innovation and Entrepreneurship of China Coal Science and Engineering Group Co.Ltd.(2018-TDMS011)。
文摘During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.
基金supported by the Program for Changjiang Scholars and Innovative Research Team in University of China under contract No,IRT0420the National Natural Science Foundation of China under contract No.50409015.
文摘The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two cases are simulated and compared with the experimental data. It shows that the RNG turbulence model can give an appropriate prediction for the configuration of equilibrium scour hole, and it is applicable to this situation. The local scour mechanism around submarine pipelines including the flow structure, shear stress distribution and pressure field is then analyzed and compared with experiments. For further comparison and validation, especially for the flow structure, a numerical calculation employing the large eddy simulation （LES） is also conducted. The numerical results of RNG demonstrate that the critical factor governing the equilibrium profile is the seabed shear stress distribution in the case of bed load sediment transport, and the two-equation RNG turbulence model coupled with the law of wall is capable of giving a satisfying estimation for the bed shear stress. Moreover, the piping phenomena due to the great difference of pressure between the upstream and downstream parts of pipelines and the vortex structure around submarine pipelines are also simulated successfully, which are believed to be the important factor that lead to the onset of local scour.
文摘Stochastic dynamic analysis of the nonlinear system is an open research question which has drawn many scholars'attention for its importance and challenge.Fokker–Planck–Kolmogorov(FPK)equation is of great significance because of its theoretical strictness and computational accuracy.However,practical difficulties with the FPK method appear when the analysis of multi-degree-offreedom(MDOF)with more general nonlinearity is required.In the present paper,by invoking the idea of equivalence of probability flux,the general high-dimensional FPK equation related to MDOF system is reduced to one-dimensional FPK equation.Then a cell renormalized method(CRM)which is based on the numerical reconstruction of the derived moments of FPK equation is introduced by coarsening the continuous state space into a discretized region of cells.Then the cell renormalized FPK(CR-FPK)equation is solved by difference method.Three numerical examples are illustrated and the effectiveness of proposed method is assessed and verified.
基金Project(10472134 ,50490274 ,50534030) supported by the National Natural Science Foundation of China
文摘The fragmentation test of granite subjected to strain rate of 10~010~2s~ -1 was carried out using split Hopkinson pressure bar(SHPB) whose diameter is 75 mm, where half-sine loading waveform was performed. The sieving statistics results of the fragments show that the distribution of the fragments is a fractal, and the fractal dimension values fall into the range of 1.22.4. The correlation analysis between the fractal dimension and the logarithm of the energy density shows that they have approximately linear relation. Finally, based on damage theory and scale invariant principle, the fragmentation model with renormalization method was put forward, and the fractal dimension value predicted with the model was compared with the test results. It is found that the fractal dimension value obtained from the improved fragmentation model is more reasonable.
基金supported by the National Natural Science Foundation of China under Grant No.12175030
文摘In this paper,we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group(fRG)approach.The f RG is a nonperturbative continuum field approach,in which quantum,thermal and density fluctuations are integrated successively with the evolution of the renormalization group(RG)scale.The f RG results for the QCD phase structure and the location of the critical end point(CEP),the QCD equation of state(EoS),the magnetic EoS,baryon number fluctuations confronted with recent experimental measurements,various critical exponents,spectral functions in the critical region,the dynamical critical exponent,etc,are presented.Recent estimates of the location of the CEP from first-principle QCD calculations within f RG and Dyson-Schwinger equations,which pass through lattice benchmark tests at small baryon chemical potentials,converge in a rather small region at baryon chemical potentials of about 600 MeV.A region of inhomogeneous instability indicated by a negative wave function renormalization is found withμ_(B)■420 MeV.It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments could arise from the increasingly sharp crossover in the regime of low collision energy.
基金Supported by the National Natural Science Foundation of China（50574090） the ＂973＂ Plan（2006CB202210）+1 种基金 Scientific Research Project of Ministry of Education（106084） the Foundation of Qinglan Project of Jiangsu Province
文摘Adopted the fractal tree-like failure model, and established the renormalization group transform function of fractured fault, and investigated the mechanism of water-inrush from fault, and found out the critical probability of water-inrush from fault caused by fault fracture. The results indicate： when the failure rate P is less than the critical failure rate Pc=0.206 3, the failure of the system is just partial. When P is more than the critical failure rate Pc=0.206 3, the random distributed crannies concentrate to certain domain of attraction （such as the maximum shear stress face in the fault） gradually. The process will continue until the crannies run-through, forming conductivity channel, and cause water-inrush from fault.
