New exact solitary-wave special solutions for the nonlinear dispersive K(m, n) equations

In this paper, we study the nonlinear dispersive K(m, n) equations: u_t + (u^m)_x − (uⁿ)_xxx = 0 which exhibit solutions with solitary patterns. New exact solitary solutions are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the decomposition method in K(m, n) equations. The nonlinear equations K(m, n) are studied for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of K(m, n) equations are established.     

Exact special solitary solutions with compact support for the nonlinear dispersive K(m, n) equations

The nonlinear dispersive K(m, n) equations, u_t−(u^m)_x−(uⁿ)_xxx = 0 which exhibit compactons: solitons with compact support, are studied. New exact solitary solutions with compact support are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the decomposition method in K(m, n) equations. General formulas for the solutions of K(m, n) equations are established.     

Numerical study of sediment transport in turbulent two-phase flows around an obstacle

This paper numerically investigates the transport of dissolved and particulate pollutants in turbulent channel flows. We present a predictive hydrodynamic model in order to explore the dispersion phenomenon of a pollutant injected at a free surface around an obstacle. The air/water interface was modeled using the volume of fluid method (VOF). Numerical results agree well with experimental data and the penetration of pollutant released at different inlet positions of the channel is studied. The Lagrangian tracking of individual particles was performed, and the transport and deposition of various particle size, density and velocity in the channel were analyzed. The standard k–ε turbulence model was chosen for this simulation.We found that large particles with a density of 1600 kg/m³, a velocity of 2 m/s and a diameter higher than 70 mm are deposited around the obstacle and near the end sill of the channel, while particles of very small size (lower than 5 mm) remain suspended in the flow and arrive at the outlet of the channel without any deposition rate. This factor must be taken into account during the discharge of effluents and pollutants in coastal water.     

Effects of CO2 concentration and moisture content of sugar-free media on the tissue-cultured plantlets in a large growth chamber

The dynamic fluctuations of CO₂ concentration in the tissue culture growth chamber after transplantation of petunia, chrysanthemum and tomato plantlets were recorded with a real-time control system to determine the critical CO₂ concentration levels of 35 μl l^?1 at which CO₂ enrichment is needed. The experimental data showed that the tissue-cultured plantlets of petunia, chrysanthemum and tomato had the same CO₂ concentration dynamics. The results indicated that CO₂ enrichment was proper on the second day after transplantation. Petunia plantlets were used to conduct experiments under PPFD of 80 μmol m^?2 s^?1, and CO₂ concentrations of 350 ± 50 μl l^?1, 650 ± 50 μl l^?1 and 950 ± 50 μl l^?1 as well as medium moisture contents of 60%, 70% and 80%, with the result that plantlets grew better under CO₂ concentration of 650 ± 50 μl l^?1 than under the other two concentrations with all the different media water contents. Three media water contents under the same CO₂ concentration produced plantlets with the same quality. The impacts of CO₂ concentrations on plantlets are more important than those of the media water contents. Sugar-free tissue culture, as compared with the conventional culture, showed that CO₂ enrichment to 350 ± 50 μl l^?1 can promote the growth of the cultured plantlets. Sugar-free tissue culture produced healthy plantlets with thick roots, almost equivalent to the common plantlets.     

Environmental flows for the Yangtze Estuary based on salinity objectives

Environmental flows based on the salinity objectives for China’s Yangtze Estuary were quantified to assess the impacts of changing freshwater inflow on the estuarine ecosystem. The salinity objectives for three benthos habitats in the Yangtze Estuary were studied to determine their requirements during the most critical period of the year. The temporal variation in the natural monthly river discharge represented the temporal variation of the ecological objectives used to maintain natural flow regimes. A numerical model, coupled a hydrodynamic processes model with a salinity model and validated using field data of tidal height, current velocity, and salinity at different stations, was developed to simulate the spatial distribution of salinity as a function of the variation in freshwater inflows. The prediction results of the proposed model agreed well with the field data. Considering the salinity objectives for the different habitats, the environmental flow requirements for the Yangtze Estuary were determined. Annual environmental flows should be 9.63 × 10¹¹, 6.32 × 10¹¹, and 4.70 × 10¹¹ m³ for the high, medium, and minimum objectives, which are equivalent to 104%, 68%, and 50% of the annual river discharge, respectively. The periods from September to November should be considered as the critical seasons to maintain the minimum environmental flows in the Yangtze Estuary.     

Adaptive network fuzzy inference system modeling for the input selection and prediction of anaerobic digestion effluent quality

This paper presents the development and evaluation of three adaptive network fuzzy inference system (ANFIS) models for a laboratory scale anaerobic digestion system outputs with varied input selection approaches. The aim was the investigation of feasibility of the approach-based-control system for the prediction of effluent quality from a sequential upflow anaerobic sludge bed reactor (UASBR) system that produced a strong nonlinearship between its inputs and outputs. As ANFIS demonstrated its ability to construct any nonlinear function with multiple inputs and outputs in many applications, its estimating performance was investigated for a complex wastewater treatment process at increasing organic loading rates from 1.1 to 5.5 g COD/L d. Approximation of the ANFIS models was validated using correlation coefficient, MAPE and RMSE. ANFIS was successful to model unsteady data for pH and acceptable for COD within anaerobic digestion limits with multiple input structure. The prediction performance showed a high feasibility of the model-based-control system on the anaerobic digester system to produce an effluent amenable for a consecutive aerobic treatment unit.     

Fractional dynamics of systems with long-range interaction

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/∣n − m∣^α+1. Continuous medium equation for this system can be obtained in the so-called infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of motion of the particles into a partial differential equation with the Riesz fractional derivative of order α, when 0 < α < 2. Few models of coupled oscillators are considered and their synchronized states and localized structures are discussed in details. Particularly, we discuss some solutions of time-dependent fractional Ginzburg–Landau (or nonlinear Schrodinger) equation.     

Environmental flow requirements for integrated water resources allocation in the Yellow River Basin,China

Based on the classification and regionalization of the ecosystem, multiple ecological management objectives and the spatial variability of the environmental flow requirements of the Yellow River Basin were analyzed in this study. The summation rule was used to calculate water consumption requirements and the compatibility rule, i.e., “maximum” principle, was also adopted to estimate the non-consumptive use of water in the river basin. The environmental flow requirements for integrated water resources allocation were determined by identifying the natural and artificial water consumption in the Yellow River Basin. The results indicated that the annual minimum environmental flow requirements amounted to 317.62 × 10⁸ m³, which represented 54.76% of the natural river flows, while for the environmental flow requirements for the integrated water resources allocation were 262.47 × 10⁸ m³, which represented 45.25% of the natural river flows. The highest percentage of environmental flow requirements was 93.64% for the river ecosystem. It can be concluded that the primary concerns should be put on the downstream river water requirements to determine the environmental flows for integrated water resources allocation in a river basin.     

Stimulated Raman scattering in the presence of trapped particle instability

The behaviour of electron gas in a laser plasma corona is studied in the presence of stimulated Raman scattering (SRS). The 1D Vlasov–Maxwell model describing plasma relevant to the experiment PALS (Prague Asterix Laser System), where the nanosecond iodine laser with the wavelength of first harmonic λ_vac = 1.3152 and with the power density in the focal spot I = 10²⁰ W/m² is in operation. For the solution of Vlasov equation for the electron distribution function a Fourier–Hermite transform method is used. For the numerical stabilization a small collision term is added to the Vlasov equation keeping its value realistic for the condition relevant to the PALS experiment. The dominant wave modes in our model are both the backward (SRS-B) and the forward (SRS-F) Raman scattering, each of them accompanied by the forward going electron plasma wave. Several mechanisms were identified such as the SRS-B plasma wave spectral broadening due to a trapped particle instability (TPI) or the formation of an electrostatic quasi-mode by non-resonant interaction of SRS-B and SRS-F plasma waves.     

On “P” property and the column-W property

P-matrices play an important role in the well-posedness of a linear complementarity problem (LCP). Similarly, the well-posedness of a horizontal linear complementarity problem (HLCP) is closely related to the column-W property of a matrix k-tuple.In this paper we first consider the problem of generating P-matrices from a given pair of matrices. Given a matrix pair (D, F) where D is a square matrix of order m and matrix F has m rows, “what are the conditions under which there exists a matrix G such that (D + FG) is a P-matrix?”. We obtain necessary and sufficient conditions for the special case when the column rank of F is m ? 1. A decision algorithm of complexity O(m²) to check whether the given pair of matrices (D, F) is P-matrisable is obtained. We also obtain a necessary and an independent sufficient condition for the general case when rank(F) is less than m ? 1.We then generalise the P-matrix generating problem to the generation of matrix k-tuples satisfying the column-W property from a given matrix (k + 1)-tuple. That is, given a matrix (k + 1)-tuple (D₁, … ,D_k, F), where D_js are square matrices of order m and F is a matrix having m rows, we determine the conditions under which the matrix k-tuple (D₁ + FG₁, … ,D_k + FG_k) satisfies the column-W property. As in the case of P-matrices we obtain necessary and sufficient conditions for the case when rank(F) = m ? 1. Using these conditions a decision algorithm of complexity O(km²) to check whether the given matrix (k + 1)-tuple is column-W matrisable is obtained. Then for the case when rank(F) is less than m ? 1, we obtain a necessary and an independent sufficient condition.For a special sub-class of P-matrices we give a polynomial time decision algorithm for P-matrisability. Finally, we obtain a geometric characterisation of column-W property by generalising the well known separation theorem for P-matrices.     

Fast Rectangular Matrix Multiplication and Applications

First we study asymptotically fast algorithms for rectangular matrix multiplication. We begin with new algorithms for multiplication of ann×nmatrix by ann×n²matrix in arithmetic timeO(n^ω),ω=3.333953…, which is less by 0.041 than the previous record 3.375477…. Then we present fast multiplication algorithms for matrix pairs of arbitrary dimensions, estimate the asymptotic running time as a function of the dimensions, and optimize the exponents of the complexity estimates. For a large class of input matrix pairs, we improve the known exponents. Finally we show three applications of our results:   (a) we decrease from 2.851 to 2.837 the known exponent of the work bounds for fast deterministic (NC) parallel evaluation of the determinant, the characteristic polynomial, and the inverse of ann×nmatrix, as well as for the solution to a nonsingular linear system ofnequations,   (b) we asymptotically accelerate the known sequential algorithms for the univariate polynomial composition mod xⁿ, yielding the complexity boundO(n^1.667) versus the old record ofO(n^1.688), and for the univariate polynomial factorization over a finite field, and   (c) we improve slightly the known complexity estimates for computing basic solutions to the linear programming problem withmconstraints andnvariables.     

Inverse dynamics of underactuated mechanical systems: A simple case study and experimental verification

Underactuated systems are featured by fewer control inputs than the degrees-of-freedom, m < n. The determination of an input control strategy that forces such a system to complete a set of m specified motion tasks is a challenging task, and the explicit solution existence is conditioned to differential flatness of the problem. The flatness-based solution denotes that all the 2n states and m control inputs can be algebraically expressed in terms of the m specified outputs and their time derivatives up to a certain order, which is in practice attainable only for simple systems. In this contribution the problem is posed in a more practical way as a set of index-three differential–algebraic equations, and the solution is obtained numerically. The formulation is then illustrated by a two-degree-of-freedom underactuated system composed of two rotating discs connected by a torsional spring, in which the pre-specified motion of one of the discs is actuated by the torque applied to the other disc, n = 2 and m = 1. Experimental verification of the inverse simulation control methodology is reported.     

Freshwater inflow requirements for the protection of the critical habitat and the drinking water sources in the Yangtze River Estuary,China

Freshwater inflow requirements (FIRs for short), which considered the requirements for protection of drinking water sources as well as the first-grade state protection wildlife (Acipenser sinensis) in larval periods, were analyzed in this paper for the Yangtze River Estuary, China. Based on the different levels of salinity objectives and the relationship between salinity and the freshwater inflows, the FIRs for the Yangtze River Estuary were determined. The estuary FIRs were determined based on the habitat ecosystem health from April to November with minimum and medium levels, from March to December with high level; and on the requirement of protection of drinking water sources in other months of the year, accordingly. Combined the salinity objectives of drinking water sources and critical habitat in the Yangtze River Estuary, the FIRs for the estuary are calculated to be 938.2 × 10⁹, 729.4 × 10⁹ and 615.5 × 10⁹ m³ in the whole year with different levels, which is equal to 100.8%, 78.4% and 66.2% of the average annual river discharge for the Yangtze River Estuary, respectively. Annual river discharges can satisfy the medium and minimum levels of FIRs for the estuary. However, the temporal variation of the actual runoff has distinct difference from the FIRs for the estuary in critical periods (May, July and August) for the habitat ecosystem, 5% of the FIRs for the estuary should be maintained from December to February for protection of drinking water sources.     

Study of wave–wind interaction at a seawall using a numerical wave channel

This paper presents the study on wind and waves interactions at a seawall using a numerical wave channel. The numerical experiments were conducted for wave overtopping of a 1/4 sloping seawall using several conditions of incident waves and wind speeds. The numerical results were verified against laboratory data in a case for wave overtopping without wind effects. The interaction of waves and wind was analyzed in term of mean wave quantities, overtopping rate and variation of wind velocity at some selected locations. The results showed that the overtopping rate was strongly affected by wind and the wind field was also significantly modified by waves. There exists an effective range of wind speed in comparison with the local shallow wave speed at the breaking location, which gives significant effects to the wave overtopping rates. The maximum of wind adjustment coefficient f_w for wave overtopping rate was strongly related to the mean overtopping rate in the case for no wind. This study also showed that when the mean overtopping rate was greater than 5 × 10⁻⁴ m³/s/m, the maximum of wind adjustment coefficient f_w approached to a specific value of about 1.25.     

On the positive definite solutions of nonlinear matrix equation X + A⋆ X−δA = Q

In this paper we consider the positive definite solutions of nonlinear matrix equation X + A^⋆X^−δA = Q, where δ ∈ (0, 1], which appears for the first time in [S.M. El-Sayed, A.C.M. Ran, On an iteration methods for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001) 632–645]. The necessary and sufficient conditions for the existence of a solution are derived. An iterative algorithm for obtaining the positive definite solutions of the equation is discussed. The error estimations are found.     

Simulación numérica del flujo turbulento de aire con gotas dispersas de agua a través de separadores de torres de refrigeración

This work presents a numerical study on the turbulent flow of air with dispersed water droplets in separators of mechanical cooling towers. The averaged Navier-Stokes equations are discretised through a finite volume method, using the Fluent and Phoenics codes, and alternatively employing the turbulence models k ? ?, k ? ω and the Reynolds stress model, with low-Re version and wall enhanced treatment refinements. The results obtained are compared with numerical and experimental results taken from the literature. The degree of accuracy obtained with each of the considered models of turbulence is stated. The influence of considering whether or not the simulation of the turbulent dispersion of droplets is analyzed, as well as the effects of other relevant parameters on the collection efficiency and the coefficient of pressure drop. Focusing on four specific eliminators (‘Belgian wave’, ‘H1-V’, ‘L-shaped’ and ‘Zig-zag’), the following ranges of parameters are outlined: 1 ≤ U_e ≤ 5 m/s for the entrance velocity, 2 ≤ D_p ≤ 50 μm for the droplet diameter, 650 ≤ Re ≤ 8.500 for Reynolds number, and 0.05 ≤ P_i ≤ 5 for the inertial parameter. Results reached alternately with Fluent and Phoenics codes are compared. The best results correspond to the simulations performed with Fluent, using the SST k ? ω turbulence model, with values of the dimensionless scaled distance to wall y⁺ in the range 0.2 to 0.5. Finally, correlations are presented to predict the conditions for maximum collection efficiency (100 %), depending on the geometric parameter of removal efficiency of each of the separators, which is introduced in this work.     

Space–time symmetry violation,configuration mixing model and E-infinity theory

We have studied the time reversal symmetry violation on the bases of the configuration mixing model and E-infinity theory. With the use of the Cabibbo angle approximation, we have presented the transformation matrix in terms of the golden ratio (?), and shown that the time reversal symmetry violation is described by the configuration mixing of the unstable and stable manifolds (W^u, W^s). The magnitude of the mixing for the weak interaction field is given by the expression sin² θ_T(theor) ≈ sin⁴ θ_C(theor) ≈ (?)¹² = 3.105 × 10^?3, which is compared to the Kaon decay experiment ～2.3 × 10^?3. We have also discussed the space–time symmetry violation by using the CPT theorem.     

Magnetohydrodynamic stationary and oscillatory convective stability in a mushy layer during binary alloy solidification

For the case of solidification of a bottom cooled binary alloy, the magnetohydrodynamic stationary and oscillatory convective stability in the mushy layer is investigated analytically using normal mode linear stability analysis. In the limit of large Stefan number (S_t), a near–eutectic approximation with large far field temperature is considered in the present research. To ascertain the instability in the mushy layer, the strength of the superimposed magnetic field is so chosen that it corresponds to a given mush Hartmann number (Ha_m) of the problem. The results are presented for various values of mush Hartmann numbers in the range, 0 ≤ Ha_m ≤ 50. The critical Rayleigh number for stationary convection shows a linear relationship with increasing Ha_m. The magnetohydrodynamic effect imparts a stabilizing influence during stationary convection. In comparison to that of the stationary convective mode, the oscillatory mode appears to be critically susceptible at higher values of β (β = S_t/℘² ϒ², ℘ is the compositional ratio, ϒ = 1 + S_t/℘), and vice versa for lower β values. Analogous to the behavior for stationary convection, the magnetic field also offers a stabilizing effect in oscillatory convection and thus influences global stability of the mushy layer. Increasing magnetic strength shows reduction in the wavenumber and in the number of rolls formed in the mushy layer.     

New families of exact soliton-like solutions and dromion solutions to the (2+1)-dimensional higher-order Broer–Kaup equations

Using homogeneous balance method we obtain Bäcklund transformation (BT) and a linear partial differential equation of higher-order Broer–Kaup equations. As a result, new soliton-like solutions and new dromion solution and other exact solutions of (2 + 1)-dimensional higher-order Broer–Kaup equations are given. By analyzing a soliton-like solution, we get some dromions solutions. This method, which can be generalized to some (2 + 1)-dimensional nonlinear evolution equations, is simple and powerful.     

Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlevé-II equations

Using the idea of transformation, some links between (2 + 1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev–Petviashvili (KP) equation, generalized (2 + 1)-dimensional break soliton equation and (2 + 1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2 + 1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived.