Study on the critical stress threshold of weakly cemented sandstone damage based on the renormalization group method

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.

Renormalization group methods for a Mathieu equation with delayed feedback

This paper presents the application of the renormalization group （RG） methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equations, and then obtain the approximate solutions by solving the corresponding RG equations. It shows that the approximate solutions obtained from the RG method are superior to those from the conventionally perturbation methods.

Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory

In this paper,we mainly investigate three topics on the renormalization group(RG)method to singularly perturbed problems:1)We will present an explicit strategy of RG procedure to get the approximate solution up to any order.2)We will refer that the RG procedure can,in fact,be used to get the normal form of differential dynamical systems.3)We will also present the approximating center manifolds of the perturbed systems,and investigate the long time asymptotic behavior by means of RG formula.

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate:Formalism and Application to Azulene

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.

Off-site trimer superfluid on a one-dimensional optical lattice

The Bose-Hubbard model with an effective off-site three-body tunneling,characterized by jumps towards one another,between one atom on a site and a pair atoms on the neighborhood site,is studied systematically on a one-dimensional（1D） lattice,by using the density matrix renormalization group method.The off-site trimer superfluid,condensing at momentum k = 0,emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model.Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from[Phys.Rev.A81,011601（R）（2010）]is stable in the thermodynamic limit.The off-site trimer superfluid phase,the partially off-site trimer superfluid phase and the Mott insulator phase are found,as well as interesting phase transitions,such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase.Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.

Lattice Boltzmann method and RANS approach for simulation of turbulent flows and particle transport and deposition

Using the lattice-Boltzmann computational approach in conjunction with the Reynolds averaged Navier-Stokes （RANS） model, several turbulent flows and the transport and deposition of particles in different passages were studied. The new lattice Boltzmann method （LBM） solved the RANS equations coupled with the standard and renormalization group k-E turbulence models. In particular, the LBM formulation was augmented by the addition of two transport equations for the probability distribution function of populations of k and 8. The discrete random walk model was used to generate the instanta- neous turbulence fluctuations. For turbulent channel flows, the analytical fits to the root mean-square velocity fluctuations obtained by the direct numerical simulation of the turbulent flow were used in the analysis. Attention was given to the proper evaluation of the wall normal turbulent velocity fluctuations particularly near the wall. The simulation results were compared with the available numerical simulation and experimental data. The new LBM-RANS model is shown to provide a reasonably accurate description of turbulent flows and particle transport and deposition at modest computational cost.

Simulation of the spin-boson model with superconducting phase qubit coupled to a transmission line

Based on the rapid experimental developments of circuit QED,we propose a feasible scheme to simulate the spin-boson model with superconducting circuits,which can be used to detect quantum Kosterlitz-Thouless(KT) phase transition.We design the spinboson model by using a superconducting phase qubit coupled to a semi-infinite transmission line,which is regarded as a bosonic reservoir with a continuum spectrum.By tuning the bias current or the coupling capacitance,the quantum KT transition can be directly detected through tomography measurement on the states of the phase qubit.We also estimate the experimental parameters using the numerical renormalization group method.

Analytical and Numerical Studies of Quantum Plateau State in One Alternating Heisenberg Chain

By using the coupled duster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the aiternating chain is a gapped dimerized state when the parameter a exceeds a critical point ac. The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field When a 〉 ac. In addition to the m = 0 plateau state, the results of density matrix renormaiization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if a 〉 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.