A principal stress method of stress analysis

The equations of equilibrium in a stress field as given by Lamé are compared with those given by Cauchy. The (P ? Q and P ? R) terms of the Lamé equations identified by the new words detend and double detend are invariant for any point in a stress field. The principal stresses are defined as real stress components. The $\text{?Xx}\text{?x}$ terms of the Cauchy equations are considered as imaginary force components. Real and imaginary stress and force components are differentiated by the differences between ray vectors, as for example a force which has only one real value and direction, and diffuse vectors, as for example a gradient, which has a real value in any direction. Shear is differentiated from detend value by its variation with the direction in which it is taken. Shear is found to be an imaginary component of force parallel to a plane.The photoelastic equidetend (isochromatic) and isoclinic maps of a plane stress field define, for any point, a gradient triangle with the three maximum gradients, Δ(P ? Q) ΔP and Δ ? Q, for its sides. Five quantities, the detend (P ? Q), the ratio of the detend to its gradient (r₄), the ratio (r₃) of the isoclinic normal ds₃ to the stress axis direction change along its length dα, the direction of the equidetend normal (θ) and the orientation of an isoclinic line (ω) with reference to a principal stress direction, determine each gradient triangle. Five equations which define elements of the gradient triangle in terms of the five measurable quantities, are developed. Definition of the triangle can be complete with two of the five measurable quantities or two of the five equations omitted. Graphic integration of principal stress changes along any line in a stress field can be made by plotting the line straight and measuring the area swept out by the normal projections, along the line, of the sides of the gradient triangle, after it has been rotated through 90 degrees.Properties of the gradient triangle are used to solve several symmetrical stress problems and to integrate along two lines through a stress field.     

New types of topological superconductors under local magnetic symmetries

We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries, in which the time-reversal symmetry is broken, but its combinations with certain crystalline symmetries, such as , , and , are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the or superconducting wire, which is characterized by a chiral Z^c invariant. More interestingly, we also find two types of totally new TSC phases in the and superinducting wires, which are beyond the known AZ class, and are characterized by a helical Z^h invariant and Z^h⊕Z^c invariants, respectively. In the Z^h TSC phase, Z pairs of Majorana zero modes (MZMs) are protected at each end. In the case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving or symmetry are presented to illustrate their novel TSC properties and MZMs.     

Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of $\text{∫}\text{0}\text{t}$s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.     

Stability criteria for certain classes of nonlinear difference equations

The general mth order difference equation X(n+m)+a₁X(n+m?1)+…+a_mX(n) = F[n,X(n),…,X(n+m?1)] is considered. The stability properties of its solutions are studied using the discrete form of Liapunov's direct method. A quadratic form is selected as a possible Liapunov function V(n,X) and a scheme is developed for determining appropriate conditions on this function to insure that its total difference ΔV(n,X) is negative semi-definite or negative definite with respect to the difference equation. The approach is applied to the fourth-order difference equation in full detail to illustrate the method for determining the conditions which imply either uniform stability or uniform asymptotic stability and specific results are obtained. Several comments on, and extensions of, the work done by Puri and Drake for the cases m = 2 and m = 3 are presented.The results of the present approach in the homogeneous case where F[n,X(n),…,X(n+m?1)] = 0 are compared with the usual Schur-Cohn criteria and are shown to be at least as good.     

Polymer stretch in two-phase microfluidics: Effect of wall wettability

Polymer stretching in two-phase microfluidics is investigated by dissipative particle dynamics. The flow patterns can be controlled by wall wettability, flowrate ratio between two phases, and Reynolds number (Re). For neutral and partially wettable walls, segmented flows are formed and polymer stretching can be controlled by Re and segment length. At high Re, stratified flows are observed and the extension ratio can be tuned by the flowrate ratio. For nonwettable walls, slug flows are formed and polymer stretching can be controlled by Re and slug length. At high Re or flowrate ratio, annular flows are observed and high extension ratio can be easily attained.     

A general equation of state: Equations for ammonia and steam

This paper is a continuation of a previous paper published in this JOURNAL. The basic idea in the two papers is to enlarge the assemblage of thermodynamic states by including the so-called “metastable” states. Considering a system, in one or two phases, which has a single type of transformation, the writer develops an equation of state of the form η = a + by + cp + dpv + (e + fv + gp + hpv) In T, where p, v, T are three independent variables, and a, b, c, etc. are constants.The latent heat at p, T = constant is λ_P,T = I (v₂ -v₁) [b+db+(f+hp) InT), which is derived from the equation of state.The available thermodynamic data on ammonia and steam are used to check these equations. It is found that within the saturated region the agreement is quite satis factory, whereas for the superheated region the agreement is not so good.     

Optimal tensegrity structures in bending: The discrete Michell truss

This paper provides the closed form analytical solution to the problem of minimizing the material volume required to support a given set of bending loads with a given number of discrete structural members, subject to material yield constraints. The solution is expressed in terms of two variables, the aspect ratio, ρ^-1, and complexity of the structure, q (the total number of members of the structure is equal to q(q+1)). The minimal material volume (normalized) is also given in closed form by a simple function of ρ and q, namely, V=q(ρ^-1/q-ρ^1/q). The forces for this nonlinear problem are shown to satisfy a linear recursive equation, from node-to-node of the structure. All member lengths are specified by a linear recursive equation, dependent only on the initial conditions involving a user specified length of the structure. The final optimal design is a class 2 tensegrity structure. Our results generate the 1904 results of Michell in the special case when the selected complexity q approaches infinity. Providing the optimum in terms of a given complexity has the obvious advantage of relating complexity q to other criteria, such as costs, fabrication issues, and control. If the structure is manufactured with perfect joints (no glue, welding material, etc.), the minimal mass complexity is infinite. But in the presence of any joint mass, the optimal structural complexity is finite, and indeed quite small. Hence, only simple structures (low complexity q) are needed for practical design.     

Mathematical study of h-index sequences

This paper studies mathematical properties of h-index sequences as developed by Liang [Liang, L. (2006). h-Index sequence and h-index matrix: Constructions and applications. Scientometrics,69(1), 153–159]. For practical reasons, Liming studies such sequences where the time goes backwards while it is more logical to use the time going forward (real career periods). Both type of h-index sequences are studied here and their interrelations are revealed. We show cases where these sequences are convex, linear and concave. We also show that, when one of the sequences is convex then the other one is concave, showing that the reverse-time sequence, in general, cannot be used to derive similar properties of the (difficult to obtain) forward time sequence. We show that both sequences are the same if and only if the author produces the same number of papers per year. If the author produces an increasing number of papers per year, then Liang’s h-sequences are above the “normal” ones. All these results are also valid for g- and R-sequences. The results are confirmed by the h-, g- and R-sequences (forward and reverse time) of the author.     

Walsh Operational Matrices for Fractional Calculus and Their Application to Distributed Systems

The Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems. A new set of orthogonal functions is derived from Walsh functions. By using the new functions, the generalized Walsh operational matrices corresponding to √s, √(s²+ 1), e^-s and e^-√s etc. are established. Several distributed parameter problems are solved by the new approach.     

Direct projection to latent variable space for fault detection

Partial least squares (PLSs) often require many latent variables (LVs) T to describe the variations in process variables X correlated with quality variables Y, which are obtained via the traditional nonlinear iterative PLS (NIPALS) optimal solution based on (X, Y). Total projection to latent structures (T-PLSs) performs further decomposition to extract LVs T_y directly related to Y from T, which are obtained by the PCA optimal solution based on the predicted value of Y. Inspired by T-PLS, combined with practical process characteristics, two fault detection approaches are proposed in this paper to solve problems encountered by T-PLS. Without the NIPALS, (X, Y) are projected into the latent variable space determined by main variations of Y directly. Furthermore, the structure and characteristics of several modified methods in statistical analysis are studied based on calculation procedures of solving PCA, PLS and T-PLS optimization problems, and the geometric significance of the T-PLS model is demonstrated in detail. Simulation analysis and case studies both indicate the effectiveness of the proposed approaches.     

Stabilities and Settling Times of Nonlinear and Time-varying Feedback Systems

The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-varying gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k₀+k₁(t)+k₂(t)g(bd) where g(bd) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-varying gains are L¹(0, t8) functions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the output of the system, is also employed to determine the settling time.     

Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations

The synchronous control of a class of disturbed chaotic Lurie systems is probed in. The conception of L_r-synchronization of drive-respond systems is presented. Via Lyapunov function analysis and comparison principle, L_r synchronous controller of the drive-respond systems under perturbation is given and its robustness is also discussed. Barbalat lemma is further used to derive the adaptively synchronous controller for the unknown disturbance situation and the globally asymptotical synchronization is realized. All designed controllers are verified by the simulations and the given controllers are linear, which are convenient and can produce rapid convergence speed of the error systems.     

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H_∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H_∞ performance is proposed. It can be applied to solve an H_∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H_∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H_∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.     

Chain matrix decompositions,continued fractions and the optimal inhomogeneous ladder networks

Studies of two-element-kind ladder networks are well known in the classical literature, among them, the most celebrated ones are due to Cauer. Driving point immittance function synthesis by using continued fractions to obtain the series and shunt arm L-C element values is a standard and routine work. The idea of introducing a class of more general networks, the inhomogeneous ladder networks, was first developed by Lee and Brown, and subsequently the synthesis techniques of such a network were established.In this paper, new results are found such as: (1) the Iff. conditions of the existence of an inhomogeneous ladder network by a given chain matrix of the network satisfying: (a) determinant of the chain matrix is 1; (b) the zeros of A(s) and z^?1B(s) or A(s) and y^?1C(s) alternate with respect to [z(s)y(s), k] with an appropriate leading set of zeros of A(s); (c) the poles of A(s) and z^?1B(s) or A(s) and y^?1C(s) are the poles of z(s)y(s) of multiplicity of n and n?1, where n the number of sections of ladder networks; (2) the Iff. condition for the inhomogeneous ladder network to be optimal is that it be antimetrical, whereas for the extended class of inhomogeneous ladder networks it is symmetrical, where an optimal inhomogeneous ladder network is defined as the corresponding network with the minimum sum of immittance levels in the series and shunt arms; (3) algorithms of synthesis procedures were developed as the by-products of the Theorems.     

Thoriated tungsten filaments

The rate of evaporation of electrons, ν_e, from a thoriated tungsten filament depends on the temperature T and on θ, the fraction of the surface covered by thorium atoms. The relation of ν_e to θ and T has been given by Brattain and Becker. From ν_e the change in contact potential V of the filament surface produced by the adsorbed thorium can be calculated by the Boltzmann equation. Knowing σ the number of thorium atoms per cm.³, the dipole moment M of each is given by V = 2τσM. By an equation already used for Cs films on tungsten, the 2-dimensional equation of state of the adsorbed film can be calculated from M. Then by Gibbs' adsorption equation the relation of the atom evaporation rate ν_a to θ and T can be determined. It is thus calculated that in the range from θ = 0.2 to θ = 0.6, ν_a varies in proportion to ?^Hθ where H = 8.1 in good agreement with the value H = 7.8 given by Brattain and Becker's measurements. A recalculation of the data of numerous experiments in 1921–1923, using the new relations of ν_e to θ₁ gives data on ν_a as a function of T and θ in good agreement with the values of ν_a calculated from ν_e.The diffusion coefficients of Th through tungsten crystals, along grain boundaries and over the free filament surface, are calculated. A theory is given for the cause of the variation in the surface diffusion coefficient with σ. The probable mechanism of the production of the metallic thorium within the filament is discussed. At 2400° the thorium which arrives at the surface along grain boundaries, for some unknown reason, does not spread out over the surface as it does at lower temperatures (1900–2100°).     

Rational approximation of three-dimensional digital filters

Two techniques are developed for approximating a given three-dimensional (3-D) digital filter by a 3-D rational function. The one is by a general 3-D rational function and the other by a 3-D rational function which is separable in the denominator. Each technique relies on the use of mixed first and second information, in the form of a finite portion of the impulse response and its autocorrelation sequence. The approximation is performed by solving a set of linear equations. The separable-denominator approximation is more advantageous due to the guaranteed stability and reduced amount of calculations.     

Changes in velocity profile according to blood viscosity in a microchannel

Red blood cells (RBCs) are important to dictate hemorheological properties of blood. The shear-thinning effect of blood is mainly attributed to the characteristics of the RBCs. Variations in hemorheological properties alter flow resistance and wall shear stress in blood vessels. Therefore, detailed understanding of the relationship between the hemorheological and hemodynamic properties is of great importance. In this study, blood viscosity and blood flow were simultaneously measured in the same microfluidic device by monitoring the flow-switching phenomenon. To investigate blood flows according to hemorheological variations, the flow rate of blood samples (RBCs suspended in autologous plasma, dextran-treated plasma, and in phosphate buffered saline solution) was precisely controlled with a syringe pump. Velocity profiles of blood flows were measured by using a micro-particle image velocimetry technique. The shape of velocity profiles was quantified by using a curve-fitting equation. It is found that the shape of the velocity profiles is highly correlated with blood viscosity. To demonstrate the relationship under ex vivo conditions, biophysical properties and velocity profiles were measured in an extracorporeal rat bypass loop. Experimental results show that increased blood viscosity seems to induce blunt velocity profile with high velocity component at the wall of the microchannel. Simultaneous measurement of blood viscosity and velocity profile would be useful for understanding the effects of hemorheological features on the hemodynamic characteristics in capillary blood vessels.     

Temperature distribution in toroidal electrical coils of rectangular cross section

The essential content of a recent paper by the present writer comprises a comprehensive discussion of the physical bases underlying derivation of formulas for calculating the temperature distribution T, maximum temperature T_m and average temperature T_a in a toroidal electrical coil of rectangular cross section, internally generated heat and change of wire resistance with temperature being taken into account. Illustratively, the solution for the boundary value condition of constant surface temperature and uniform equivalent thermal conductivity was obtained.For the most part, however, problems that arise in practice are not encompassed in the comparatively simple boundary conditions of constant temperature. Experiment shows that in general the boundary condition is $\text{T ? T′ = ?}\text{K?}\text{?n}$; whereof n denotes the outward drawn normal to the coil surface, $\text{K = (}\text{k}{}_{\mathrm{n}}\text{h}\text{)}$ the ratio of the equivalent thermal conductivity in the direction of n to the emissivity of the boundary surface, and T and T′ are the corresponding temperatures in the coil surface and the immediately adjacent ambient medium. Again, it frequently ensues in practice that the thermal conductivity is substantially different in the directions of the two principal axes of the cross section.In the present paper formulas for T, T_m, and T_a are obtained for electrical coils of ratio of external to internal radius greater than (roughly) two whereof (i) the thermal conductivity is different in the directions of the two principal axes of the cross section, (ii) K is different on but constant over each of the four faces of the coil, and (iii) no restriction is made as to T′ except that over each face it be expressible in a generalized Fourier series. Determination of T is posed as a boundary-value problem in the mathematical theory of heat; the formal solution of T effected by expansions in orthogonal functions; and T_m and T_a then determined through use of their known relationships with T. The resulting formulas are in the form of rapidly-converging singly-infinite trigonometric-hyperbolic series. Illustrative of application of these general formulas, the maximum temperatures in a coil of given dimensions subject to two different sets of surface conditions are calculated and found to be in excellent agreement with the known measured values.The just-mentioned formulas encompass practically all cases encountered in practice except those coils which do not satisfy the restriction as to ratio of radii. For these latter formulas for T, T_m, and T_a are obtained pursuant to conditions of (i) equivalent thermal conductivity different in the directions of the two principal axes of the cross section, (ii) K, and likewise T′, different on but constant over each of the four faces of the coil. These formulas are in the form of rapidly-converging singly-infinite trigonometric- Bessel function (of zero order) series: Illustratively, the maximum temperature in a coil of given dimensions is calculated and found to be in excellent agreement with the known measured value.     

Novel antimicrobial activity of a dichloromethane extract obtained from red seaweed Ceramium rubrum (Hudson) (Rhodophyta: Florideophyceae) against Yersinia ruckeri and Saprolegnia parasitica,agents that cause diseases in salmonids

BackgroundEnteric red mouth disease and Saprolegniasis, which are caused by the bacteria Yersinia ruckeri and the oomycete Saprolegnia parasitica, respectively, are important illnesses that affect salmonid farming. Sanitary problems in farms are addressed by the prevention of disease outbreaks or by the treatment of diseases with chemicals. Environmental and governmental restrictions, toxicity and high treatment costs limit the use of drugs. Marine organisms, such as algae, sponges and corals, have developed an antimicrobial defense strategy based on the production of bioactive metabolites. Among these organisms, seaweeds offer a particularly rich source of potential new drugs. Hence, many pharmacologically active substances have been isolated from seaweeds. In the Ceramium genus, Ceramium rubrum has been emphasized by several authors for its antimicrobial properties. Based on this background, the present study focused on the antimicrobial activity of a lipophilic extract of C. rubrum on Y. ruckeri and S. parasitica.ResultsThe alga, collected from the Pacific coast of Chile, underwent an ethanol extraction, and the concentrated extract was partitioned between water and dichloromethane. From the dichloromethane extract, fatty acids, fatty acid esters, one hydrocarbon and phytol were identified by Gas Chromatography–Mass Spectrometry (GC/MS) analysis. The antimicrobial study showed that the whole extract was more active than the individual components, which suggests a strong synergistic effect among the components.ConclusionsThese results may constitute a basis for promising future applied research that could investigate the use of C. rubrum seaweed as a source of antimicrobial compounds against fish pathogens.