Nonlinear acoustic approach to material characterisation of polymers and composites in tensile tests

The paper reports on experimental study of elastic nonlinearity of polymers and glass fibre-reinforced (GFR-) composites in a wide range of tensile stress applied (up to a fracture limit). Focused slanted transmission mode (FSTM) of air-coupled ultrasound is adapted for remote generation and detection of flexural waves in the samples of plastics. Local noncontact measurements of flexural wave velocity as a function of static strain are used to calculate the second-order nonlinearity parameters beta2 and study their behaviour through a loading cycle. Molecular untangling and crazing phenomena are identified, respectively, with maxima of positive and negative beta2 in thermoplastics. In composites, mechanics of fibre-matrix interaction is considered for brittle and plastic fractures. Hysteresis in velocity variation during loading-unloading cycle is used as an indicator of residual defect accumulation.     

Some Methods Based on the D-Gap Function for Solving Monotone Variational Inequalities

The D-gap function has been useful in developing unconstrained descent methods for solving strongly monotone variational inequality problems. We show that the D-gap function has certain properties that are useful also for monotone variational inequality problems with bounded feasible set. Accordingly, we develop two unconstrained methods based on them that are similar in spirit to a feasible method of Zhu and Marcotte based on the regularized-gap function. We further discuss a third method based on applying the D-gap function to a regularized problem. Preliminary numerical experience is also reported.     

Preliminary results of the cross-section measurement of e<Superscript>+</Superscript>e<Superscript>−</Superscript> → φ(1020)η process with the CMD-3 detector at VEPP-2000 collider

We report preliminary results on the cross section of the process e⁺e^? → φ(1020)η measured at 30 center-of-mass energy points in the range from 1.59 up to 2.0 GeV. Data analysis is based on the integrated luminosity of 22 pb^?1 collected with the CMD-3 detector in 2011–2012. The obtained cross section agrees with the BaBar measurement and has better statistical accuracy.     

Zur Berechnung des Wärmeübergangs bei einphasiger freier Konvektion in der Nähe des kritischen Zustandes

Zusammenfassung Experimentelle Ergebnisse zum überkritischen Wärmeübergang weisen für den Zustandsbereich nahe dem kritischen Punkt zum Teil große Abweichungen von der für unterkritische Fluide bekannten Abhängigkeit des Wärmeübergangskoeffizienten von der Wärmestromdichte auf. Am Beispiel des Kältemittels RC318 (C₄F₈) wird gezeigt, daß auch diese Ergebnisse mit den bekannten Beziehungen zwischen der Nußelt-, der Grashof- und der Prandtl-Zahl beschrieben werden können, wenn der thermische Ausdehnungskoeffizient und die spezifische Wärme in Gr bzw. Pr durch Differenzenquotienten ersetzt und zwei zusätzliche Parameter zur Beschreibung der Dichteänderung innerhalb der beheizten Fluidzone eingeführt werden. Da ein Teil der in den Kennzahlen benötigten Stoffwerte von RC318 im interessierenden Zustandsbereich nicht bekannt ist, werden die fehlenden Stoffwerte mit Hilfe des allgemeinen Korrespondenzprinzips berechnet.

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Calculation of free convective heat transfer near the critical state

For certain conditions free convective heat transfer from horizontal tubes to fluids near the critical state differs widely from the well-known dependency of heat transfer coefficient from heat flux. It is shown that experiments with refrigerant RC318 (C₄F₈) even for these conditions can be described by one of the often applied relationships between Nusselt and Rayleigh numbers, if the special form of density variation within the heated region of the fluid is taken into account. Most of the thermophysical properties of RC318 being unknown near the critical state, thermodynamic similarity considerations are used to calculate these data.

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Formelzeichen F Korrekturfaktor - R individuelle Gaskonstante - T Temperatur - Z Realfaktor - Gr, Nu, Pr Kennzahlen - a Temperaturleitzahl - c_v, C_p spezifische Wärme - d Rohrdurchmesser - g Erdbeschleunigung - h spezifische Enthalpie - m Molekülmasse - p Druck - q Wärmestromdichte - u innere Energie - v spezifisches Volumen - Wärmeübergangskoeffizient - _k Riedel-Parameter - thermischer Ausdehnungskoeffizient - Realanteil - Differenz zwischen einer Zustandsgröße des Fluids an der Heizwand und außerhalb der beheizten Zone - Asymmetrieparameter - Viskosität, dynamische - Wärmeleitzahl - Viskosität, kinematische - Dichte Indizes-hochgestellt normierte Größe - * auf den Wert am kritischen Punkt normierte Größe - 0 im Zustand des idealen Gases Indizes-tiefgestellt B, + Bezugswert - f Fluid außerhalb der beheizten Zone - k am kritischen Punkt - W an der Wand Herrn Professor Dr.-Ing. H. Glaser, Stuttgart, zum 70. Geburtstag gewidmet.Die Autoren danken Herrn Prof. Dr. K. Bier für die unterstützung der Arbeit und für wertvolle Diskussionsbeiträge.     

Strongly nonlinear shear perturbations in discrete and continuous cubic nonlinear systems

Systems with constraints, the masses in which move only along guides, can execute strongly nonlinear vibrations. This means that nonlinear phenomena manifest themselves at arbitrary small deviations from equilibrium. The form of vibrations of a single mass is described by elliptical Jacobi functions. The spectrum of these vibrations is found. With an increase in amplitude, the period of vibrations decreases. We deduce equations of strongly nonlinear vibrations of a chain of connected masses. In the continuum limit, we obtain a new nonlinear equation in partial derivatives. We devise transformation of variables leading to linearization of this equation. We implemented a factorization procedure that decreases the order of the equation in partial derivatives from second to first. Exact solutions to the first-order equation describe the slow evolution of the displacement profile in a distributed system. In the absence of preliminary tension of elastic elements in the continued model, traveling waves cannot be achieved; however, time-oscillating solutions like standing waves are possible. We obtain an equation for a field of strongly nonlinear deformations. Its exact solution describes periodic movement in time and space. As well, the period of time oscillations decreases with an increase in amplitude, and the spatial period, in contrast, increases. The product of the vibration frequency multiplied by the spatial period is a constant that depends on the deformation energy. We propose a scheme of the mechanical system producing strongly nonlinear torsional vibrations. We experimentally measured the period of torsional vibrations of a single disc. We show that with an increase in amplitude in the process of vibration attenuation, an increase in the period occurs, which agrees with calculations. We measure the shapes of nonlinear vibrations of a chain of connected discs. A strongly nonlinear behavior of the chain is observed.     

Lower bounds for positive and negative parts of measures and the arrangement of singularities of their Laplace transforms

For a real measure with variation V(x) satisfying the estimate V(x) ≤ c ₀ exp(Cx) and for the Laplace transform holomorphic in the disk {¦ -C¦ ≤ C} and having at least one pole of order m, we obtain lower bounds for the positive and negative parts of the measure V _± (x) > cx ^m , x > x ₀. We establish lower bounds for V _+- (x) on “short” intervals. Applications to number theory of the results obtained are considered.     

A Hybrid Approximate Extragradient – Proximal Point Algorithm Using the Enlargement of a Maximal Monotone Operator

We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extragradient and proximal methods. Furthermore, the algorithm uses elements in the enlargement (proposed by Burachik, Iusem and Svaiter) of the operator defining the problem. One of the important features of our approach is that it allows significant relaxation of tolerance requirements imposed on the solution of proximal point subproblems. This yields a more practical proximal-algorithm-based framework. Weak global convergence and local linear rate of convergence are established under suitable assumptions. It is further demonstrated that the modified forward-backward splitting algorithm of Tseng falls within the presented general framework.     

Semismooth Newton method for the lifted reformulation of mathematical programs with?complementarity constraints

We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation is semismooth and BD-regular at the solution under reasonable assumptions. Thus, fast local convergence can be obtained by applying the semismooth Newton method. Moreover, it turns out that the squared residual of the Lagrange system is continuously differentiable (even though the system itself is not), which opens the way for a natural globalization of the local algorithm. Preliminary numerical results are also reported.     

On local convergence of sequential quadratically-constrained quadratic-programming type methods,with an extension to variational problems

We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Optim. 12, 949–978, 2002) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadratic convergence of the primal-dual sequence was established by Fukushima, Luo and Tseng (SIAM J. Optim. 13, 1098–1119, 2003) under the assumption of convexity, the Slater constraint qualification, and a strong second-order sufficient condition. We obtain a new local convergence result, which complements the above (it is neither stronger nor weaker): we prove primal-dual quadratic convergence under the linear independence constraint qualification, strict complementarity, and a second-order sufficiency condition. Additionally, our results apply to variational problems beyond the optimization case. Finally, we provide a necessary and sufficient condition for superlinear convergence of the primal sequence under a Dennis-Moré type condition. Research of the second author is partially supported by CNPq Grants 300734/95-6 and 471780/2003-0, by PRONEX–Optimization, and by FAPERJ.