Modulational instability of a resonantly polariton condensate in discrete lattices

We study modulational instability of a resonantly polariton condensate in a discrete lattice.Employing a discrete gain-saturation model,we derive the dispersion relation for the modulational instability by means of the linear-stability analysis.Effects of the pumping strength,the nonlinearity,the strength of the detuning,and the coupling strength on the modulation instability are investigated.It is found that the interplay between these parameters will dramatically change the modulational instability condition.We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.

A Few Discrete Lattice Systems and Their Hamiltonian Structures,Conservation Laws

With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie–Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore,we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively.

Application of Exp-Function Method to Discrete Nonlinear Schrdinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.

Localized self-trapping in the two-dimensional discrete molecular lattice with the interaction between Frenkel excitons and phonons

We investigate the interactions of lattice phonons with Frenkel exciton, which has a small radius in a twodimensional discrete molecular lattice, by the virtue of the quasi-discreteness approximation and the method of multiplescale, and obtain that the self-trapping can also appear in the two-dimensional discrete molecular lattice with harmonic and nonlinear potential. The excitons＇ effect on the molecular lattice does not distort it but only causes it to localize which enables it to react again through phonon coupling to trap the energy and prevent its dispersion.

Periodic,quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein-Gordon lattice

We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.

Darboux Transformation and Explicit Solutions for Discretized Modified Korteweg-de Vries Lattice Equation

The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.

Numerical investigation of refracturing with/without temporarily plugging diverters in tight reservoirs

Refracturing is an importa nt technique to tap the potential of reservoirs and boost production in depleted oil and gas fields.However,fracture propagation during refracturing,including both conventional refracturing and temporary-plugging refracturing remains poorly understood,especially for cases with non-uniform distribution of formation pressure due to long-term oil production and water injection.Therefore,taking pilot tests of refracturing with sidetracking horizontal wells in tight reservoirs in the Changqing Oilfield,China as an example,we establish a three-dimensional numerical model of conventional refracturing and a numerical model of temporary-plugging refracturing based on the discrete lattice method.Non-uniform distributions of formation pressure are imported in these models.We discuss the effects of key operating parameters such as injection rate,cluster spacing,and number of clusters on the propagation of multi-cluster fractures for conventional refracturing.For temporaryplugging refracturing,we examine the impacts of controlling factors such as the timing and number of temporary plugging on fracture propagation.In addition,we analyze a field case of temporaryplugging refracturing using well P3 in the Changqing Oilfield.The results show that fractures during re fracturing tend to propagate preferentially and dominantly in the depleted areas.Improved stimulation effect can be obtained with an optimal injection rate and a critical cluster spacing.The proposed model of temporary-plugging refracturing can well describe the temporary plugging of dominant existingfractures and the creation of new-fractures after fracturing fluid is forced to divert into other clusters from previous dominant clusters.Multiple temporary plugging can improve the balanced propagation of multi-cluster fractures and obtain the maximum fracture area.The established numerical model and research results provide theoretical guidance for the design and optimization of key operating parameters for refracturing,especially for temporary-plugging refracturing.

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.

Multiscale Homogenization Analysis of Alkali–Silica Reaction (ASR) Effect in Concrete

The alkali silica reaction (ASR) is one of the major long-term deterioration mechanisms occurring in con- crete structures subjected to high humidity levels, such as bridges and dams. ASR is a chemical reaction between the silica existing inside the aggregate pieces and the alkali ions from the cement paste. This chemical reaction produces ASR gel, which imbibes additional water, leading to gel swelling. Damage and cracking are subsequently generated in concrete, resulting in degradation of its mechanical proper- ties. In this study, ASR damage in concrete is considered within the lattice discrete particle model (LDPM), a mesoscale mechanical model that simulates concrete at the scale of the coarse aggregate pieces. The authors have already modeled successfully ASR within the LDPM framework and they have calibrated and validated the resulting model, entitled ASR-LDPM, against several experimental data sets. In the pre- sent work, a recently developed multiscale homogenization framework is employed to simulate the macroscale effects of ASR, while ASR-LDPM is utilized as the mesoscale model. First, the homogenized behavior of the representative volume element (RVE) of concrete simulated by ASR-LDPM is studied under both tension and compression, and the degradation of effective mechanical properties due to ASR over time is investigated. Next, the developed homogenization framework is utilized to reproduce experimental data reported on the free volumetric expansion of concrete prisms. Finally, the strength degradation of prisms in compression and four-point bending beams is evaluated by both the mesoscale model and the proposed multiscale approach in order to analyze the accuracy and computational ef - ciency of the latter. In all the numerical analyses, different RVE sizes with different inner particle realiza- tions are considered in order to explore their effects on the homogenized response.

Extended Hyperbolic Function Rational Expansion Algorithm with Symbolic Computation to Construct Solitary Wave Solutions of Discrete mKdV Lattice

With the aid of Maple, the extended hyperbolic function rational expansion method is used to construct explicit and exact travelling solutions for the discrete mKdV lattice. As a result, many solutions are obained which include kink-shaped solitary wave solutions, bell-shaped solitary wave solutions and singular solitary wave solutions.

Assessment and optimization of fracture-karst cave connectivity in horizontal well hydraulic fracturing of carbonate reservoirs

The karst cave serves as the primary storage space in carbonate reservoirs.Simultaneously connecting multiple karst caves through hydraulic fracturing is key to the efficient development of carbonate reservoirs.However,there is lack of systematic research on the mechanisms and influencing factors of fracture propagation in car-bonate rocks.This paper established models including karst cave models,single natural fracture-cave models,and multiple natural fracture-cave models based on the discrete lattice method.It thoroughly studied how geological and operational factors affect the fracture propagation and the connectivity of karst caves.The final step involved establishing a prototype well model and optimizing operation parameters.The research indicates that an increase in the Young's modulus and pore pressure of karst cave could facilitate hydraulic fracture connecting with caves.When the pore pressure is lower than that in the matrix,it will generate a repulsive effect on hydraulic fractures.The natural fracture along the hydraulic fracture path significantly facilitates the connection with caves.When the wellbore azimuth is less than 60℃,the fracture's diversion radius is small,and hydraulic fractures primarily connect with karst cave through natural fractures.When the wellbore azimuth exceeds 60℃,the fracture's diversion radius increases.Under the combined action of hydraulic fractures and natural fractures,the stimulated volume of the karst cave noticeably increases.Under the same liquid volume,increasing the injection rate could enhance the cave stimulated volume.Combining the findings from numerical simulation studies resulted in the development of a diagram that depicts the connectivity of karst caves,providing valuable insight for hydraulic fracturing operations in carbonate reservoirs.

Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.

Numerical simulation of polygonal particles moving in incompressible viscous fluids

A two-dimensional coupled lattice Boltzmann immersed boundary discrete element method is introduced for the simulation of polygonal particles moving in incompressible viscous fluids. A collision model of polygonal particles is used in the discrete element method. Instead of a collision model of circular particles, the collision model used in our method can deal with particles of more complex shape and efficiently simulate the effects of shape on particle–particle and particle–wall interactions. For two particles falling under gravity, because of the edges and corners, different collision patterns for circular and polygonal particles are found in our simulations. The complex vortexes generated near the corners of polygonal particles affect the flow field and lead to a difference in particle motions between circular and polygonal particles. For multiple particles falling under gravity, the polygonal particles easily become stuck owing to their corners and edges, while circular particles slip along contact areas. The present method provides an efficient approach for understanding the effects of particle shape on the dynamics of non-circular particles in fluids.

Mechanics of granular column collapse in fluid at varying slope angles

This paper investigates the effect of initial volume fraction on the runout characteristics of collapse of granular columns on slopes in fluid. 2-D sub-grain scale numerical simulations are performed to understand the flow dynamics of granular collapse in fluid. The discrete element method（DEM） technique is coupled with the lattice Boltzmann method（LBM）, for fluid-grain interactions, to understand the evolution of submerged granular flows. The fluid phase is simulated using multiple-relaxation-time LBM（LBM-MRT） for numerical stability. In order to simulate interconnected pore space in 2-D, a reduction in the radius of the grains（hydrodynamic radius） is assumed during LBM computations. The collapse of granular column in fluid is compared with the dry cases to understand the effect of fluid on the runout behaviour. A parametric analysis is performed to assess the influence of the granular characteristics（initial packing） on the evolution of flow and run-out distances for slope angles of 0 °, 2.5°, 5 ° and 7.5 °. The granular flow dynamics is investigated by analysing the effect of hydroplaning, water entrainment and viscous drag on the granular mass. The mechanism of energy dissipation, shape of the flow front, water entrainment and evolution of packing density is used to explain the difference in the flow characteristics of loose and dense granular column collapse in fluid.