Neural networks analysis of free laminar convection heat transfer in a partitioned enclosure

The feasibility of using neural networks (NNs) to predict the complete thermal and flow variables throughout a complicated domain, due to free convection, is demonstrated. Attention is focused on steady, laminar, two-dimensional, natural convective flow within a partitioned cavity. The objective is to use NN (trained on a database generated by a CFD analysis of the problem of a partitioned enclosure) to predict new cases; thus saving effort and computation time. Three types of NN are evaluated, namely General Regression NNs, Polynomial NNs, and a versatile design of Backpropagation neural networks. An important aspect of the study was optimizing network architecture in order to achieve best performance. For each of the three different NN architectures evaluated, parametric studies were performed to determine network parameters that best predict the flow variables.A CFD simulation software was used to generate a database that covered the range of Rayleigh number Ra = 10⁴–5 × 10⁶. The software was used to calculate the temperature, the pressure, and the horizontal and vertical components of flow speed. The results of the CFD were used for training and testing the neural networks (NN). The robustness of the trained NNs was tested by applying them to a “production” data set (1500 patterns for Ra = 8 × 10⁴ and 1500 patterns for Ra = 3 × 10⁶), which the networks have never been “seen” before. The results of applying the technique on the “production” data set show excellent prediction when the NNs are properly designed. The success of the NN in accurately predicting free convection in partitioned enclosures should help reduce analysis-time and effort. Neural networks could potentially help solve some cases in which CFD fails to solve because of numerical instability.     

Numerical simulation of magnetohydrodynamic buoyancy-induced flow in a non-isothermally heated square enclosure

Numerical simulation of magnetohydrodynamic (MHD) buoyancy-induced heat transfer and fluid flow has been analyzed in a non-isothermally heated square enclosure using finite volume method. The bottom wall of enclosure were heated and cooled with a sinusoidal function and top wall was cooled isothermally. Vertical walls of the enclosure were adiabatic. Effects of Rayleigh number (Ra = 10⁴, 10⁵ and 10⁶), Hartman number (Ha = 0, 50 and 100) and amplitude of sinusoidal function (n = 0.25, 0.5 and 1) on temperature and flow fields were analyzed. It was observed that heat transfer was decreased with increasing Hartmann number and decreasing value of amplitude of sinusoidal function.     

Computational modelling of fluid structure interaction at nano-scale boundaries with modified Maxwellian velocity distribution

The soft collisions among fluid–fluid and fluid-wall molecules are modeled from first principles. In particular, the assumption of Maxwellian distribution of velocities for thermalized molecules, in both parallel and perpendicular directions to the wall, has been re-evaluated with supporting experimental and/or numerical evidence.It is proposed that the normal component of molecular velocity post collision is conserved for all fluid molecules. The slip effect at the wall boundary, introduced by the surface roughness, is accounted by an accommodation coefficient f. A moving least square method is used to calculate macroscopic velocity values. The influence of molecular interaction on the macroscopic velocity distribution is investigated at 40 MPa and 300 K for slit pore, inclined and stepped wall configurations. The accommodation coefficient values f = 0, 0.07, 0.257, 0.45, 0.681 and 1; and acceleration values ranging from zero to 1 × 10¹¹ m/s² and 250 × 10¹¹ m/s² are used for comparison.The distribution of macroscopic velocity parallel to the wall is studied to observe the effect of the slip behaviour. The detailed study of average of velocity values at various magnitudes of acceleration has shown an evidence of characteristic low and high speed of molecular flows that is considered as significant and a comparison is sought with an equivalent laminar and turbulent flow style behaviour. The two dimensional vector and contour plots of macroscopic velocity provide further insights in understanding Continuum velocity distributions resulting from molecular fluid-wall interaction at nanoscale. The research has highlighted the need to develop molecular dynamics simulation techniques for non-periodic boundary conditions.     

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.     

Analysis and improvement of a hash-based image encryption algorithm

The security of digital image attracts much attention recently. A hash-based digital image encryption algorithm has been proposed in Ref. [1]. But both the theoretical analysis and computer simulation show the characteristic of diffusion is too weak to resist Chosen Plaintext Attack and Known Plaintext Attack. Besides, one bit difference of the plain pixel will lead to only one corresponding bit change of the cipher pixel. In our improved algorithm, coupled with self-adaptive algorithm, only one pixel difference of the plain-image will cause changes of almost all the pixels in the cipher-image (NPCR > 98.77%), and the unified average changing intensity is high (UACI > 30.96%). Both theoretical analysis and computer simulation indicate that the improved algorithm can overcome these flaws and maintain all the merits of the original one.     

Vacuum polarization in light two-electron atoms and ions

A general theory of the vacuum polarization in light atomic and muon-atomic systems is considered. We derive the closed analytical expression for the Uehling potential and evaluate corrections on vacuum polarization for the 1¹S-state of the two-electron ³He and ⁴He atoms and for some two-electron ions, including the Li⁺, Be²⁺, B³⁺ and C⁴⁺ ions. The correction for vacuum polarization in two-electron He atoms has been evaluated as ΔE_ueh ≈ 7.253 ± 0.0025 × 10⁻⁷ a.u. The analogous corrections in the two-electron He-like ions rapidly increase with the nuclear charge Q (ΔE_ueh ≈ 2.7061 × 10⁻⁶ a.u. for the Li⁺ ion and ΔE_ueh ≈ 2.3495 × 10⁻⁵ a.u. for the C⁴⁺ ion). The corresponding corrections have also been evaluated for the electron–nucleus and electron–electron interactions.     

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.     

Commutativity and self-duality: Two tales of one equation

The mathematical expressions for the commutativity or self-duality of an increasing [0, 1]² → [0, 1] function F involve the transposition of its arguments. We unite both properties in a single functional equation. The solutions of this functional equation are discussed. Special attention goes to the geometrical construction of these solutions and their characterization in terms of contour lines. Furthermore, it is shown how ‘rotating’ the arguments of F allows to convert the results into properties for [0, 1]² → [0, 1] functions having monotone partial functions.     

Bifurcation and chaos in discrete-time predator–prey system

The discrete-time predator–prey system obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory. And numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including period-3, 5, 6, 7, 8, 9, 10, 12, 18, 20, 22, 30, 39-orbits in different chaotic regions, attracting invariant circle, period-doubling bifurcation from period-10 leading to chaos, inverse period-doubling bifurcation from period-5 leading to chaos, interior crisis and boundary crisis, intermittency mechanic, onset of chaos suddenly and sudden disappearance of the chaotic dynamics, attracting chaotic set, and non-attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The computations of Lyapunov exponents confirm the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.     

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.     

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.     

On generalized Jordan 1-derivation in rings

Let n ⩾ 1 be a fixed integer and let R be an (n + 1)!-torsion free 1-ring with identity element e. If F, d:R → R are two additive mappings satisfying F(xⁿ⁺¹) = F(x)(x¹)ⁿ + xd(x)(x¹)ⁿ⁻¹ + x²d(x)(x¹)ⁿ⁻²+ ⋯ +xⁿd(x) for all x ∈ R, then d is a Jordan 1-derivation and F is a generalized Jordan 1-derivation on R.     

Integrals,Quantum Galois Extensions,and the Affineness Criterion for Quantum Yetter–Drinfel'd Modules

In this paper we shall generalize the notion of an integral on a Hopf algebra introduced by Sweedler, by defining the more general concept of an integral of a threetuple (H, A, C), where H is a Hopf algebra coacting on an algebra A and acting on a coalgebra C. We prove that there exists a total integral γ: C → Hom(C, A) of (H, A, C) if and only if any representation of (H, A, C) is injective in a functorial way, as a corepresentation of C. In particular, the quantum integrals associated to Yetter–Drinfel'd modules are defined. Let now A be an H-bicomodule algebra, ^H$\text{Y}$$\text{D}$_A the category of quantum Yetter–Drinfel'd modules, and B = {a ∈ A|∑S^− 1(a_〈1〉)a_{〈 − 1〉} ⊗ a_〈0〉 = 1_H ⊗ a}, the subalgebra of coinvariants of the Verma structure A ∈ ^H$\text{Y}$$\text{D}$_A. We shall prove the following affineness criterion: if there exists γ: H → Hom(H, A) a total quantum integral and the canonical map β: A ⊗ _B A → H ⊗ A, β(a ⊗ _B b) = ∑S^− 1(b_〈1〉)b_{〈 − 1〉} ⊗ ab_〈0〉 is surjective (i.e., A/B is a quantum homogeneous space), then the induction functor – ⊗ _B A: $\text{M}$_B → ^H$\text{Y}$$\text{D}$_A is an equivalence of categories. The affineness criteria proven by Cline, Parshall, and Scott, and independently by Oberst (for affine algebraic groups schemes) and Schneider (in the noncommutative case), are recovered as special cases.     

Validación numérica del comportamiento cíclico de conexiones interiores en estructuras con forjados reticulares

Several approaches are investigated to model interior reinforced concrete waffle-flat-plate-column connections. A model is proposed that provides very good results with reasonable low computational cost. The proposed model is validated with the experimental results obtained on a 3/5 scale specimen, subjected to quasi-static in cyclic loads up to collapse. To this end, the non-linear advanced theory of reinforced concrete is applied on a three-dimensional finite element model and non-linear analysis are conducted. Both fiber and layer elements are used for the one-dimensional and bi-dimensional components respectively. The main results of the simulation were: (i) the capacity curve obtained through out a push-over analysis with displacement control, (ii) the hysteretic curves of the slab, and (iii) the crack patterns. A very good agreement is found between numerical and experimental results.     

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.     

Backbone fractal dimension and fractal hybrid orbital of protein structure

Fractal geometry analysis provides a useful and desirable tool to characterize the configuration and structure of proteins. In this paper we examined the fractal properties of 750 folded proteins from four different structural classes, namely (1) the α-class (dominated by α-helices), (2) the β-class (dominated by β-pleated sheets), (3) the (α/β)-class (α-helices and β-sheets alternately mixed) and (4) the (α + β)-class (α-helices and β-sheets largely segregated) by using two fractal dimension methods, i.e. “the local fractal dimension” and “the backbone fractal dimension” (a new and useful quantitative parameter). The results showed that the protein molecules exhibit a fractal behavior in the range of 1 ? N ? 15 (N is the number of the interval between two adjacent amino acid residues), and the value of backbone fractal dimension is distinctly greater than that of local fractal dimension for the same protein. The average value of two fractal dimensions decreased in order of α > α/β > α + β > β. Moreover, the mathematical formula for the hybrid orbital model of protein based on the concept of backbone fractal dimension is in good coincidence with that of the similarity dimension. So it is a very accurate and simple method to analyze the hybrid orbital model of protein by using the backbone fractal dimension.     

Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation

This paper intends to explore the bifurcation of limit cycles for planar polynomial systems with even number of degrees. To obtain the maximum number of limit cycles, a sixth-order polynomial perturbation is added to a quintic Hamiltonian system, and both local and global bifurcations are considered. By employing the detection function method for global bifurcations of limit cycles and the normal form theory for local degenerate Hopf bifurcations, 31 and 35 limit cycles and their configurations are obtained for different sets of controlled parameters. It is shown that: H(6) ⩾ 35 = 6² − 1, where H(6) is the Hilbert number for sixth-degree polynomial systems.     

On mathematical models and numerical simulation of the fluidization of polydisperse suspensions

The well-known Masliyah–Lockett–Bassoon (MLB) model for sedimentation of small particles is extended to fluidization of polydisperse suspensions. For N particle species that differ in size and density, this model leads to a first-order system of N conservation laws, which in general is of mixed (in the case N = 2, hyperbolic–elliptic) type. By a simple algebraic steady-state analysis, we derive necessary compatibility conditions on the size and density parameters that admit the formation of stationary fluidized beds. We then proceed to determine the composition of polydisperse fluidized beds of given compatible species by varying the fluidization velocity and the initial composition of the suspensions, and prove that, within the framework of the MLB model combined with the Richardson–Zaki formula, the constructed bidisperse beds always cause the equations to be hyperbolic. This means that these states are always predicted to be stable. The transient behaviour of the MLB model applied to fluidization is illustrated by three numerical examples, in which the system of conservation laws is solved for N = 2, N = 3 and N = 5, respectively. These examples illustrate the effects of bed expansion and layer inversion caused by successively increasing the applied fluidization velocity and show that the predicted fluidized states are indeed attained.     

Filter matrix based on interpolation wavelets for solving Fredholm integral equations

The interpolation wavelet is used to solve the Fredholm integral equation of the second kind in this study. Hence, by the extension of interpolation wavelets that [−1, 1] is divided to 2^N+1 (N ⩾  − 1) subinterval, we have polynomials with a degree less than M + 1 in each new interval. Therefore, by considering the two-scale relation the filter coefficients and filter matrix are used as the proof of theorems. The important point is interpolation wavelets lead to more sparse matrix when we try to solve integral equation by an approximate kernel decomposed to a lower and upper resolution. Using n-time, where (n ⩾ 2), two-scale relation in this method errors of approximate solution as O((2^−(N+1))ⁿ⁺¹). Also, the filter coefficient simplifies the proof of some theorems and the order of convergence is estimated by numerical errors.