Round-handle decomposition of S 2×S 1

A round-handle decomposition is associated with a non-singular Morse–Smale flow on 3-manifolds prime to S ²× S ¹. This decomposition has been built only for the 3-sphere S ³. In this paper we obtain the round-handle decomposition of non-singular Morse–Smale flows on S ²× S ¹, in order to get all the different fattened round handles in this manifold. Some of them include non-separating boundary components that induce the topology of the links of periodic orbits.     

A new approach to the velocity field investigation in case of the entry flow in curved pipes with circular cross section

Summary In this paper an analysis of a laminar flow in a bend preceded by the straight section is presented. The flow is supposed to be unperturbed far upstream, while far downstream it becomes fully developed. In the vicinity of the sharp junction between the, bended and the straight section, the solution is expanded in terms of integer powers ofe ^S quantity (S is reduced distance from the curvature onset along the pipe axis). The corresponding expansion coefficients were determined in order to provide the velocity field continuity across the junction.     

Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects

The steady withdrawal of an inviscid fluid of finite depth into a line sink is considered for the case in which surface tension is acting on the free surface. The problem is solved numerically by use of a boundary-integral-equation method. It is shown that the flow depends on the Froude number, F _B=m(gH ³ _B)^–1/2, and the nondimensional sink depth =H _S/H _B, where m is the sink strength, g the acceleration of gravity, H _B is the total depth upstream, H _S is the height of the sink, and on the surface tension, T. Solutions are obtained in which the free surface has a stagnation point above the sink, and it is found that these exist for almost all Froude numbers less than unity. A train of steady waves is found on the free surface for very small values of the surface tension, while for larger values of surface tension the waves disappear, leaving a waveless free surface. It the sink is a long way off the bottom, the solutions break down at a Froude number which appears to be bounded by a region containing solutions with a cusp in the surface. For certain values of the parameters, two solutions can be obtained.     

Typical flow between enclosed corotating disks and its dependence on Reynolds number

Abstract

The flow in an enclosed co‐rotating disk pair is investigated by Laser Doppler Velocimetry (LDV) measurements and flow visualizations. First, the typical flow structure at Re = 5.25 × 10⁵ and S = 0.09 is clarified. The flow fields in the r – θ and the r – z planes are both investigated and then divided into several flow regions based on the distinct flow types observed. The flow regions found in the two different planes are also compared and integrated. Second, with S fixed, the dependence of the flow field structure upon the Reynolds number is discussed. Three regimes of the r – θ plane flow with different Reynolds numbers are identified based on the measured mean velocity and spectral intensity. When Re < 1.6 × 10⁵, no solid body region is found and the flow is in a laminar regime. In the range 1.6 × 10⁵ ≤ Re ≤ 2.0 × 10⁶, the solid body region and the outer region vortices coexist, and an empirical equation is developed to estimate the number of vortices. When Re > 2.0 × 10⁶, the flow becomes turbulent. As Re increases from 9.3 × 104 to 5.25 × 10⁵, the spectral intensity initially increases and then decreases before increasing again to an even higher level, resulting in an increasing sawtooth pattern.     

Reliability of deterministic non‐linear systems subjected to stochastic dynamic excitation

Engineering structures react to exceptionally high forces caused by, for example, extreme winds, sea waves, earthquakes, avalanches, etc. in a non‐linear way, before they finally collapse. Mostly these environmental loadings cause dynamic excitations which are adequately modeled by the so‐called stochastic processes. To identify subsets of the excitation, which may trigger failure, methods based on power inputs of the stochastic excitation will be exploited. This procedure is based on the simple consideration that any excitation that maximizes the energy input into the system has the potential to adversely affect the integrity of the structure. This method considers the velocity of the displacement field of the structure and the energy dissipation induced by viscous damping, friction and hysteresis. For an efficient reliability estimation, the n‐dimensional standard normal space S^[0]∈??ⁿ, in which the stochastic excitation is modeled, is split into two disjunct subspaces S^[1]∈??^m and S^[2]∈??^n?m. The subset S^[1]∈??^m represents the space of important directions, which is identified by a procedure based on an approximation of the gradient of the energy input. Directional sampling in the subspace S^[1] and direct Monte Carlo sampling in the subspace S^[2] are combined to established an efficient estimator for the structural reliability. The proposed methodology is generally applicable to finite element models with strong non‐conservative non‐linearities. Copyright © 2010 John Wiley & Sons, Ltd.     

Compression fatigue performance of a fire resistant syntactic foam

Compression–compression fatigue test study of a fire resistant Eco-Core was conducted at two values of stress ratios (R = 10 and 5). Tests were conducted at S_min/S_o values of 0.9–0.6 for R = 10 and 0.95–0.8 for R = 5. Here S_min is the maximum compression stress and S_o is the compression strength. The study showed that Eco-Core has well defined failure modes and associated fatigue lives. The failure modes are: damage on-set; damage progression, and final failure. The damage on-set, propagation and final failure were characterized by 2%, 5% and 7% changes in compliance. The three failure modes were found to be same for both static and fatigue loadings. The endurance limit was found to be 0.72S_o, 0.75S_o and 0.76S_o, respectively for three failure modes for R = 10 and 0.81S_o, 0.82S_o and 0.82S_o, respectively for R = 5. The fatigue life is defined by a power law equation, S_min/S_o = A_oN^α. Constants of the equation were established for all three modes of failures and the two stress ratios. Finally, fatigue life was found to be less sensitive to R ratio when expressed in terms of stress range versus number of load cycles, which is similar to that of metallic materials.     

Flexural fatigue of short glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulfide

Flexural fatigue tests were conducted on injection molded glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulfide composite using four-point bending with different stress ratios and different frequencies. The fatigue behavior of this material was described. The constructed S-N curves shift their trends obviously at the maximum cyclic stress being about 80% of the ultimate flexural strength. Examinations of failure surfaces for various loading conditions show that the fatigue failure mechanisms appear to be matrix yielding at high stresses and crack growth at low stresses. Analyses of the fatigue data at various stress ratios reveal that the data at low stress superimpose to form a single curve which is nearly linear when they are plotted as stress range versus number of cycles to failure in bilogarithmic axes, while the data at high stresses also converge to yield a single curve when they are plotted as (S _max S _range)^1/2 against specimen lifetimes (S _max is the maximum stress andS _range is the stress range). These results show that for the studied material the main factor influencing the lifetime is the stress range at low stresses and the parameter (S _max S _range)^1/2 at high stresses. Comparison of fatigue data in the frequency range of 0.89–7.0 Hz was made, no significant effect of frequency on the fatigue behavior is found.     

Source-sink flow in a rotating cylinder

Summary This paper describes the axisymmetric source-sink flow in a rapidly rotating cylinder. Relative fluid motion is induced by the presence of a sink in the bottom corner and a ring source located somewhere in the fluid, at some distance from the solid boundaries. In order to neglect nonlinear effects the volumetric flow rates are assumed to be small, i.e. O(E ^1/2), with E the Ekman number of the flow. The transport from the source to the sink is carried by Ekman layers at the end caps, and a Stewartson layer at the sidewall. At the ring source a free Stewartson layer arises, in which the injected fluid is transported towards the Ekman layers. This Stewartson layer consists of layers of thicknesses E ^1/4 and E ^1/3, which both contribute to the vertical O(E ^1/2) transport. The ring source is enveloped by a ring-shaped region of cross-sectional dimensions O(E ^1/2 × E ^1/2), in which the injected fluid is rearranged before erupting into the E ^1/3 layer. As E ^1/2 E ^1/3, this region appears as an isolated singularity in the E ^1/3 layer; in fact it consists of a combination of an upward and a downward directed source, the strengths of which can be determined by transport arguments. The paper presents an analysis of the E ^1/3-layer structure on the basis of a linear theory; it also describes how the analysis can be extended to the situation in which fluid is injected through an array of sources at different heights.     

An algorithm for spectral factorization using random search techniques

An approximation method for the energy spectrum of a stationary stochastic dynamical system is presented, which allows approximate functional rational factorization.This paper is in three parts. The first deals with a theoretical problem of approximation in Hardy Spaces, whose main result is the following:Let S⁽ⁱⁿ⁾, S be positive functions belonging to L¹(R_gw), such that log S⁽ⁿ⁾ and log S belong to L¹(R_ω, dω/1 + ω²).Let h⁽ⁿ⁾, h be the outer functions of the Hardy Space H²(Π₊) such that S^(g) = |h⁽ⁿ⁾|² and S = |h|² on iR.If S⁽ⁿ⁾ n^→∝ S in L¹(R_ω), and log S⁽ⁿ⁾ n^→∝ log S in L¹(R_ω, dω/1 + ω²), then: h⁽ⁿ⁾ n^→∝ h in H²(Π₊).The second part describes an effective algorithm, using random search methods, and gives an almost sure convergence result for it.The third part treats numerically two examples, permitting comparison of this algorithm with others (whenever there are…): the first example is a problem of approximation for a nonrational process (turbulence) that was considered in Ref. 22: the second example is a problem of model reduction (automatic) considered in Ref. 4.     

Effect of particle size ratio and volume fraction on shear strength of binary granular mixture

This paper deals with the mechanical properties of a binary granular mixture: a mixture of large and small frictional particles. The binary mixture is characterized by the particle size ratio (α = D _L /D _S ≥ 1), where D _L and D _S denote the diameter of large and small particles, and the volume fraction of the small particles W _S . In order to evaluate the shear strength of such a system, a transition range (W_S^a ￡ W_S ￡ W_S^b{W_{S}^{a} \le W_{S} \le W_{S}^{b}}), where W_S^a{W_{S}^{a}} and W_S^b{W_{S}^{b}} are minimum and maximum W _S values of the range, respectively, is defined as the range in which the interaction between the small and the large particles cannot be negligible. Then a simplified packing structure model is proposed to estimate W_S^a{W_{S}^{a}} and W_S^b{W_{S}^{b}} with respect to α. A series of 2D Discrete Element simulation and physical experiment proved that the proposed method can successfully describe the shear strength transition of the densely packed granular material both in 2D and 3D. As a general trend, it also turns out that the contribution of the small particles cannot be negligible even in their small content, and the contribution of large particles disappears when their average spacing with respect to the small particle size is around 2 both in the simulation and the experiment.     

Hydromagnetic flow past a rotating porous plate in a conducting fluid rotating about a noncoincident parallel axis

Summary The hydromagnetic flow of an incompressible viscous electrically conducting fluid past a porous plate is investigated when the plate rotates with a uniform angular velocity about an axis normal to the plate and the fluid at infinity rotates with the same angular velocity about a non-coincident parallel axis. It is shown that in the presence of a uniform magnetic field parallel to the axis of rotation the boundary layer thickness decreases with an increase in either the suction at the plate or the magnetic parameter M. In the presence of suction at the plate, the velocity component u in the direction normal to the plane containing the axis of rotation of the plate and that of the fluid increases with an increase in M, while the velocity component v in the transverse direction parallel to the plane of the plate decreases with an increase in M. For a fixed value of M, at a given location u increases with an increase in the suction parameter S while v decreases with increasing S. For a fixed value of M, at a given location both u and v decrease with an increase in the blowing parameter S₁. Further, for a fixed value of S₁, at a given position u increases with an increase in M but v decreases with increasing M. It is shown that no torque is exerted by the fluid on the plate, and non-coaxial rotations of the plate and the fluid at infinity have no influence on the torque.The solution of the heat transfer equation reveals that for given values of the suction parameter S, Prandtl number P and Eckert number E, the temperature at a given point in the flow increases with increasing M. On the other hand, for fixed values of M, P and E, the temperature at a given point decreases with increasing S. No steady distribution of temperature exists when there is blowing at the plate.     

Fracture toughness anisotropy of a pyrolytic carbon

The anisotropic flexural strengths, static Young's moduli and the corresponding fracture toughnesses were measured for the three orthogonal fracture surface orientations,S _ca (interlaminar cleavage),S _ba andS _ab (layer rupture across and along the layers, respectively), of an as deposited substrate-nucleated pyrolytic carbon. BothS _ca delamination andS _ab along-layer rupture produced smooth fracture surfaces with meanK _lc values (MPam^1/2) of 0.53 forS _ca and 0.93 forS _ab , independent of notch length. A different type of behaviour was observed forS _bc across-layer fracture. Delamination cracking during failure resulted in rough fracture surfaces, crack arrests, and high apparent toughness values dependent on sample size and crack length. The nature of this induced delamination toughening is discussed.On leave from Toyohashi University of Technology, Tempaku-cho, Toyohashi 440, Japan.     

FATIGUE LIFE PREDICTION IN BENDING FROM AXIAL FATIGUE INFORMATION

Bending fatigue in the low cyclic life range differs from axial fatigue due to the plastic flow which alters the linear stress-strain relation normally used to determine the nominal stresses. An approach is presented in this report to take into account the plastic flow in calculating nominal bending stress S_bending based on true surface stress. For a given surface strain ε_S, hence the surface life (N_S), an equation is derived to express S_bending in terms of axial fatigue stress (S_axial), involving material constants c, b, N_T which are obtained from axial fatigue information and f₁ and f₂ which are functions of strain hardening exponent and depend on the geometry of cross-section. These functions are derived in closed form for rectangular and circular cross-sections. The nominal bending stress and the axial fatigue stress are plotted as a function of life (N_S) and these curves are shown for some materials of engineering interest.     

Formulation study of a patch containing propranolol by design of experiments

Objective: To evaluate the feasibility of a transdermal patch containing propranolol (PR).

Method: Skin penetration enhancers (SPEs) able to improve the skin permeability of PR were selected and a quality by design approach was applied to the development of the patch by a 2⁴ full factorial design. The permeation profile of PR from the formulations was assessed in in vitro permeation studies performed by using Franz diffusion cells and human epidermis as membrane. Finally, skin irritation was evaluated by the Draize test.

Results: N-methyl pyrrolidone (NMP) resulted as the best SPE: in addition, the critical factors influencing the PR diffusion through the human epidermis when loaded in the patch resulted in the matrix thickness (X₁, p?=?0.0957) and PR content (X₃, p?=?0.0004) which improved the flux; conversely, NMP lacked its enhancement effect when loaded in the patch and the increase in its concentration (X₄, p?=?0.006) affected the drug permeation through human epidermis. The flux of optimal formulation was 12.7?μg/cm²/h. On the basis of the steady-state concentration and clearance of PR, the estimated patch surface was 100–120 cm², since the activity of PR is related to its Senantiomer and no in vivo bioconversion occurs.

Conclusion: A patch containing (S)-PR was prepared and the (S)-PR flux (13.3?μg/cm²/h) permitted to confirm the suitability of a transdermal administration of PR. In particular, the use of a 50?μm thick methacrylic matrix containing 8% (S)-PR and 15% NMP can allow to develop a patch non-irritating to the skin, in order to ensure a constant permeation flux of PR over 48?h.     

Enhanced transdermal delivery of carvedilol using nanoemulsion as a vehicle

The aim of the present study was to develop nanoemulsion as a possible vehicle for enhanced transdermal penetration of carvedilol (CVD). For screening of nanoemulsion components, solubility of CVD in oils, surfactants and co-surfactants was determined. Various surfactants and co-surfactants were screened for their ability to nanoemulsify the selected oily phases. The obtained results indicated that Acconon CC6® had shown good nanoemulsification efficiency (minimum surfactant required S _min?=?46.52%?w/w) among the selected surfactants and further improved in presence of CO-20® (S _min?=?37.11%?w/w). The ranges of nanoemulsion existence were delineated through the construction of the pseudo-ternary phase diagram at different ratio of surfactant mixture (S/CoS), and various nanoemulsions were selected from phase diagram of S/CoS ratio 1?:?1. The effect of content of oil and S/CoS (1?:?1) on the skin permeation of CVD was evaluated through an excised wistar rat skin using Franz diffusion cell. All the nanoemulsions showed a high skin permeation rate (92.251–161.53?µg/cm²/h), good enhancement ratio (3.5–6.2) and high permeability coefficient in comparison to control groups. The optimised nanoemulsion formulation with the highest skin permeation rate (161.53?µg/cm²/h) consisted of 0.25%?w/w CVD, 12.5%?w/w Miglyol 810®, 50%?w/w Acconon CC6®/CO-20® (1?:?1) and water. The above formulation had the smallest mean globules size (9.28?nm). The superior transdermal flux of CVD may be due to nanorange size of oil globules that lead to intimate contact with the skin layer. These studies suggest that the nanoemulsion system is a promising vehicle for the transdermal delivery of CVD.     

Entropy Flow of Chemical Oscillating Reactions Involving Amino Acids

Variations of H⁺, Mn²⁺, and BrO₃^-{{\rm BrO}_3^-} during chemical oscillating reactions involving amino acids were investigated using H₂SO₄–BrO₃^-{{\rm BrO}_3^{-}} –Mn²⁺–acetone as an oscillator, and the thermodynamic functions (ΔS, ΔH, and ΔG) were calculated. The results indicated that the oscillating reaction is a process from disorder to order. In the oscillating system, the heat provided by the environment is used to increase the internal energy and entropy. When external positive entropy flow could make the system reach negative entropy flow, the system starts to oscillate and to maintain oscillations by a stable entropy.     

Dibenzothiophene‐S,S‐Dioxide‐Based Conjugated Polymers: Highly Efficient Photocatalyts for Hydrogen Production from Water under Visible Light

Three dibenzothiophene‐S,S‐dioxide‐based alternating copolymers were synthesized by facile Suzuki polymerization for visible light–responsive hydrogen production from water (> 420 nm). Without addition of any cocatalyst, FluPh2‐SO showed a photocatalytic efficiency of 3.48 mmol h^?1 g?¹, while a larger hydrogen evolution rate (HER) of 4.74 mmol h^?1 g^?1 was achieved for Py‐SO, which was ascribed to the improved coplanarity of the polymer that facilitated both intermolecular packing and charge transport. To minimize the possible steric hindrance of FluPh2‐SO by replacing 9,9′‐diphenylfluorene with fluorene, Flu‐SO exhibited a more red‐shifted absorption than FluPh2‐SO and yielded the highest HER of 5.04 mmol h^?1 g^?1. This work highlights the potential of dibenzothiophene‐S,S‐dioxide as a versatile building block and the rational design strategy for achieving high photocatalytic efficiency.     

The Design of the S2 Control Charts Based on Conditional Performance via Exact Methods

In this paper, we consider the conditional performance of the equal‐tailed and average run lengths (ARL)‐unbiased two‐sided S² charts when the in‐control variance of a normal process is estimated. We derive the exact probability distributions of the conditional ARL for the two S² charts. Then we evaluate the performance of each S² chart in terms of the percentiles, mean and standard deviation of the conditional in‐control ARL distribution. Because the parameter estimation seriously affects the conditional performance of these S² charts, we propose an exact method to design the equal‐tailed and ARL‐unbiased S² charts with desired conditional in‐control performance. The results indicate that the new ARL‐unbiased S² chart has far smaller standard deviation ARL values and the unconditional ARL values are more close to the desired value than the corresponding new equal‐tailed S² chart. Copyright © 2017 John Wiley & Sons, Ltd.     

A decomposition of the class of semiconvex games

Summary The paper studies the classSC ^N of cooperative games with player setN which have the semiconvexity property.SC ^N is decomposed into an algebraic sum of convex cones of games for which generating sets are available. The union of these sets thus forms a generating set forSC ^N . Special attention is paid to one of the considered cones, in the decomposition ofSC ^N . In particular, the so called airport savings gamesW _y, ℝ ^N , defined byw _y (S)=Σ _jεS Y _i −max _jεS Y _j for 0 ≠S⋞N, are emphasized. This work is part of the Ph.D. thesis of the first author (Derks 1991).     

Asymptotic angular stability in non-linear systems: rotation numbers and winding numbers

The asymptotic angular stability of a dynamical system may be quantified by its rotation number or its winding number. These two quantities are shown to result from different assumptions, made about the flow generating the Poincaré map which results from the sequence of homeomorphisms in S ^l. An ergodic theorem of existence a.s. of the rotation number for non-linear systems is given. The advantages and disadvantages of both the rotation and winding numbers are discussed. Numerical calculations of the distribution of rotation number and winding number arising from different initial conditions are presented for three different chaotic maps.