Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

This work elaborates upon two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980’s. The objective is, after recalling the links between these models and existing generalized continuum theories as developed in the 1960’s and subsequently, to apply the same methodology to the case of diffusion with a view to establishing generalized transport equations. Aifantis double diffusivity and conductivity theory that provides generalized mass or heat transfer equations is compared to micromorphic-type hyper-temperature and micro-entropy proposals. The double temperature and the micromorphic thermal models are shown to lead to equations more general that Cattaneo’s. The sign of the coefficient of the second time-derivative of temperature is found to differ according to both approaches. The double temperature model contains a fourth space derivative term not present in the micromorphic models. Such generalized equations can be useful, for example, in the interpretation of recent femtosecond laser experiments on metals.     

Effect of PBT molecular weight and reactive compatibilization on the dispersed‐phase coalescence of PBT/SAN blends

Poly(butylene terephthalate) (PBT)/styrene‐acrylonitrile copolymer (SAN) blends were investigated with respect to their phase morphology. The SAN component was kept as dispersed phase and PBT as matrix phase and the PBT/SAN viscosity ratio was changed by using different PBT molecular weights. PBT/SAN blends were also compatibilized by adding methyl methacrylate‐co‐glycidyl methacrylate‐co‐ethyl acrylate terpolymer, MGE, which is an in situ reactive compatibilizer for melt blending. In noncompatibilized blends, the dispersed phase particle size increased with SAN concentration due to coalescence effects. Static coalescence experiments showed evidence of greater coalescence in blends with higher viscosity ratios. For noncompatibilized PBT/SAN/MGE blends with high molecular weight PBT as matrix phase, the average particle size of SAN phase does not depend on the SAN concentration in the blends. However noncompatibilized blends with low molecular weight PBT showed a significant increase in SAN particle size with the SAN concentration. The effect of MGE epoxy content and MGE molecular weight on the morphology of the PBT/SAN blend was also investigated. As the MGE epoxy content increased, the average particle size of SAN initially decreased with both high and low molecular weight PBT phase, thereafter leveling off with a critical content of epoxy groups in the blend. This critical content was higher in the blends containing low molecular weight PBT than in those with high molecular weight PBT. At a fixed MGE epoxy content, a decrease in MGE molecular weight yielded PBT/SAN blends with dispersed nanoparticles with an average size of about 40 nm. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Undulation instability in two-dimensional foams of magnetic fluid

Two-dimensional magnetic fluid foams are cellular structures whose framework is made of magnetic fluid. The features of these equilibrated patterns are driven by a control parameter: the amplitude of the applied magnetic field. When the latter is rapidly increased, an instability occurs: the walls between cells undulate. Such an instability has also been observed in other 2D cellular structures, which exist for instance in Langmuir monolayers or in magnetic garnets thin films. In this paper we give a theoretical analysis of this instability, the issues of which are shown to be well confirmed by experiments and numerical simulations. Received: 13 October 1997 / Received in final form: 28 January 1998 / Accepted: 9 March 1998     

Fermion–Antifermion Condensate Contribution to the Anomalous Magnetic Moment of a Fundamental Dirac Fermion

We consider the contribution offermion–antifermion condensates to the anomalousmagnetic moment of a fermion in a vacuum in which suchcondensates exist. The real part of the condensatecontribution to the anomalous magnetic moment is shown to bezero. A nonzero imaginary part is obtained below thekinematic threshold for intermediatefermion–antifermion pairs. The calculation isshown to be gauge-parameter independent provided a single fermion masscharacterizes both the fermion propagator andcondensate-sensitive contributions, suggestive of adynamically generated fermion mass. The nonzeroimaginary part is then argued to correspond to the kinematicproduction of the intermediatestate Goldstone bosonsanticipated from a chiral-noninvariant vacuum. Finally,speculations are presented concerning the applicability of these results to quark electromagneticproperties.     

Biodegradable polycaprolactone–polyanhydrides blends

Biodegradable polymers based on a blend of polycaprolactone (PCL) and aliphatic polyanhydrides with various monomer lengths were prepared to obtain desired polymer blends for use as drug carriers. The physicochemical, mechanical, and drug‐release properties of these blends were investigated by various techniques to evaluate the uniformity degree of the polymer blends to establish their potential applications in drug delivery. The results demonstrated that the heat of fusion (ΔH) of the polyanhydride or the blend is increased in relation to the length of the aliphatic chain. However, the blends had different properties than pure polyanhydride, and the crystallization degree of the blends, as expressed by the ΔH, decreased in relation to the ΔH of the pure polyanhydride. Drug‐release studies from blends of PCL and aliphatic polyanhydrides demonstrated first‐order kinetics of the release rate. Polymer degradation was independent at the polyanhydride monomer length. On the basis of theoretical calculation of the interaction factor, a blend of PCL and poly(dodecanedeoic anhydride) was chosen for further elucidation of its thermal, mechanical, and degradation properties. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3781–3787, 2003     

The zero set $$\Lambda $$ of exponential polynomials and the Riesz property of its exponential system $$E_{\Lambda }$$ in $$L^2(0,T)$$

Archiv der Mathematik - Consider the class of exponential polynomials of the form $$\begin{aligned} f(z)=\sum _{n=0}^{N}\left( \sum _{k=0}^{m_n}c_{n,k}z^k\right) e^{h_n z}, \qquad 0=h_0<...     

Bubble growth predictions by the hyperbolic and parabolic heat conduction equations

A model for bubble growth in a uniformly superheated liquid is presented which is valid for both inertia and heat diffusion controlled growth. Two different heat transfer equations are considered: The Fourier (parabolic) equation and the hyperbolic heat conduction equation. It is shown that for short times, bubble growth prediction based on the Fourier equation, differs considerably from that based on the hyperbolic heat conduction equation. For long times, both predictions coincide. Using the hyperbolic heat conduction equation is important for bubble growth prediction in fluids like Helium II, in which thermal disturbances have a low speed of propagation. In such liquids the second sound effects must be considered long after the inertia and dynamic effects become unimportant.The validity of using a semi-infinite approximation to the heat conduction problem during the bubble growth period is investigated. An analytical solution in spherical coordinates reveals that the ratio between the spherical and semi-infinite solutions is a function of the Jakob number. Results of the present model, using the Fourier equation, are shown to be in better agreement with data for bubble growth in water, than other published solutions.

---

Beschreibung des Blasenwachstums durch Wärmeleitungs-Gleichungen von hyperbolischer und parabolischer Form

Zusammenfassung Es wird ein Modell für Blasenwachstum in überhitzter Flüssigkeit vorgestellt, das sowohl bei durch Trägheit als auch bei durch Wärmediffusion kontrolliertem Blasenwachstum verwendbar ist. Zwei unterschiedliche Wärmeübertragungsbeziehungen werden in Betracht gezogen: Die Fourier-Gleichung (parabolisch) und eine Wärmeleitungs-Gleichung in hyperbolischer Form.Es wird gezeigt, daß die Modellergebnisse basierend auf der Fourier-Gleichung für schnelle Blasenwachstumszeiten signifikant von vergleichbaren Ergebnissen basierend auf der hyperbolischen Gleichung abweichen, während sie für langsames Wachstum mehr oder weniger identisch sind. Die Verwendung der hyperbolischen Wärmeleitungsgleichung in Blasenwachstumsmodellen ist vor allem in Fluiden wie Helium II von Bedeutung, wo thermische Störungen eine geringe Ausbreitungsgeschwindigkeit haben. Hier müssen die second sound-Effekte noch berücksichtigt werden, wenn die dynamischen und die Einflüsse der Trägheit schon vernachlässigbar sind.Es wurde untersucht, ob die Benutzung einer semi-unendlichen Approximation des Wärmeleitungsproblems während des Blasenwachstums zulässig ist. Eine analytische Lösung in Kugelkoordinaten zeigt, daß das Verhältnis zwischen letzteren und semi-unendlichen Ergebnissen eine Funktion der Jakob-Zahl ist.Schließlich wird gezeigt, daß die Resultate des vorgestellten Modells bei Benutzung der Fourier-Gleichung experimentelle Ergebnisse von Blasenwachstum in Wasser besser wiedergeben als andere bekannte Lösungen.

---

Nomenclature a thermal diffusivity - B _s sphericity correction factor - b temperature decay coefficient - c propagation speed of thermal disturbances - E parameter, Eq. (37) - f function of the dimensionless time and bubble radius, Eq. (34) - h _v heat of evaporation - Ja Jakob number, Eq. (35) - k thermal conductivity - N /T - P pressure - P _i initial system pressure - P _v vapour pressure - Q* dimensionless heat flux (Stanton number) - q heat flux - transformed heat flux - q _wL heat flux into the liquid at the bubble boundary - R bubble radius - R* dimensionless bubble radius, Eq. (16) - R ₀ initial (critical) bubble radius - r radial coordinate - s the Laplace transform parameter - T temperature - T _i initial liquid temperature - T _s saturation temperature - T _v instantaneous bubble temperature - T ₀ initial saturation temperature,T _s (0) - T temperature difference,T _i–T _s (0) - t time - t* dimensionless time, Eq. (16) - y dimensionless distance from the bubble surface - Z constant of integration, Appendix A - a proportionality constant - temperature function, Eq. (8) - transformed temperature function - _v vapour density - _L liquid density - _vi initial vapour density - relaxation time,a/c ² - normalized temperature distribution, Eq. (15)     

Development of adaptive modeling techniques for non-linear hysteretic systems

Adaptive estimation procedures have gained significant attention by the research community to perform real-time identification of non-linear hysteretic structural systems under arbitrary dynamic excitations. Such techniques promise to provide real-time, robust tracking of system response as well as the ability to track time variation within the system being modeled. An overview of some of the authors’ previous work in this area is presented, along with a discussion of some of the emerging issues being tackled with regard to this class of problems. The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed. Particular attention is given to (1) the effects of over- and under-parameterization on parameter convergence and system output tracking performance, (2) identifiability in multi-degree-of-freedom structural systems, (3) trade-offs in setting user-defined parameters for adaptive laws, and (4) the effects of noise on measurement integration. Both simulation and experimental results indicating the performance of the parametric and non-parametric methods are presented and their implications are discussed in the context of adaptive structures and structural health monitoring.     

Multiplex Detection of Enzymatic Activity with Responsive Lanthanide‐Based Luminescent Probes

Multiplex analyte detection in complex dynamic systems is desirable for the investigation of cellular communication networks as well as in medical diagnostics. A family of lanthanide‐based responsive luminescent probes for multiplex detection is reported. The high modularity of the probe design enabled the rapid assembly of both green and red emitters for a large variety of analytes by the simple exchange of the lanthanide or an analyte‐cleavable caging group, respectively. The real‐time three‐color detection of up to three analytes was demonstrated, thus setting the stage for the non‐invasive investigation of interconnected biological processes.