Inhomogeneous Fractional Diffusion Equations

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Characterizing permanent deformation and fracture of asphalt mixtures by using compressive dynamic modulus tests

Permanent deformation and fracture may develop simultaneously when an asphalt mixture is subjected to a compressive load. The objective of this research is to separate viscoplasticity and viscofracture from viscoelasticity so that the permanent deformation and fracture of the asphalt mixtures can be individually and accurately characterized without the influence of viscoelasticity. The undamaged properties of 16 asphalt mixtures that have two binder types, two air void contents, and two aging conditions are first obtained by conducting nondestructive creep tests and nondestructive dynamic modulus tests. Testing results are analyzed by using the linear viscoelastic theory in which the creep compliance and the relaxation modulus are modeled by the Prony model. The dynamic modulus and phase angle of the undamaged asphalt mixtures remained constant with the load cycles. The undamaged asphalt mixtures are then used to perform the destructive dynamic modulus tests in which the dynamic modulus and phase angle of the damaged asphalt mixtures vary with load cycles. This indicates plastic evolution and crack propagation. The growth of cracks is signaled principally by the increase of the phase angle, which occurs only in the tertiary stage. The measured total strain is successfully decomposed into elastic strain, viscoelastic strain, plastic strain, viscoplastic strain, and viscofracture strain by employing the pseudostrain concept and the extended elastic-viscoelastic correspondence principle. The separated viscoplastic strain uses a predictive model to characterize the permanent deformation. The separated viscofracture strain uses a fracture strain model to characterize the fracture of the asphalt mixtures in which the flow number is determined and a crack speed index is proposed. Comparisons of the 16 samples show that aged asphalt mixtures with a low air void content have a better performance, resisting permanent deformation and fracture. © 2012 American Society of Civil Engineers.

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Population

2000 Mathematics Subject Classification: primary 60J80; secondary 60J85, 92C37.

Fourth-root summation of contrast over area:no end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat

Measurements of area summation for luminance-modulated stimuli are typically confounded by variations in sensitivity across the retina. Recently we conducted a detailed analysis of sensitivity across the visual field (Baldwin et al, 2012) and found it to be well-described by a bilinear “witch’s hat” function: sensitivity declines rapidly over the first 8 cycles or so, more gently thereafter. Here we multiplied luminance-modulated stimuli (4 c/deg gratings and “Swiss cheeses”) by the inverse of the witch’s hat function to compensate for the inhomogeneity. This revealed summation functions that were straight lines (on double log axes) with a slope of -1/4 extending to ≥33 cycles, demonstrating fourth-root summation of contrast over a wider area than has previously been reported for the central retina. Fourth-root summation is typically attributed to probability summation, but recent studies have rejected that interpretation in favour of a noisy energy model that performs local square-law transduction of the signal, adds noise at each location of the target and then sums over signal area. Modelling shows our results to be consistent with a wide field application of such a contrast integrator. We reject a probability summation model, a quadratic model and a matched template model of our results under the assumptions of signal detection theory. We also reject the high threshold theory of contrast detection under the assumption of probability summation over area.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Distinguishing tectonically-and gravity-driven synsedimentary deformation structures along the Apulian platform margin (Gargano Promontory, southern Italy)

Acknowledgements This work has been supported by Reservoir Characterisation Project (www.rechproject.com) and FAR Project 2014 "Characterisation and modelling of natural reservoirs of geofluids in fractured carbonate rocks", funded by the University of Camerino, coordinator Emanuele Tondi.

Internal deformation and kinematic indicators within a tripartite Mass Transport Deposit, NW Argentina

Acknowledgments This work was carried out with support from CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) – Brazil, BG-Brazil and the University of Aberdeen. We would like to thank the following geologists for their support, camaraderie and countless hours of fieldwork: Claus Fallgatter, Victoria Valdez, Carla Puigdomenech, Guilherme Bozetti, Roberto Noll Filho and Arthur Giovannini, and we thank Lorena Moscardelli and an anonymous reviewer, whose constructive comments helped to improve the manuscript.

Basement-cover tectonics, structural inheritance and deformation migration in the outer parts of orogenic belts : A view from the western Alps

Postprint

Visualization and prediction of spatial deformation using thin-plate splines in the context of scoliosis

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Active Surface Deformation Technology for Management of Marine Biofouling

Biofouling, the accumulation of biomolecules, cells, organisms and their deposits on submerged and implanted surfaces, is a ubiquitous problem across various human endeavors including maritime operations, medicine, food industries and biotechnology. Since several decades, there have been substantial research efforts towards developing various types of antifouling and fouling release approaches to control bioaccumulation on man-made surfaces. In this work we hypothesized, investigated and developed dynamic change of the surface area and topology of elastomers as a general approach for biofouling management. Further, we combined dynamic surface deformation of elastomers with other existing antifouling and fouling-release approaches to develop multifunctional, pro-active biofouling control strategies.

This research work was focused on developing fundamental, new and environment-friendly approaches for biofouling management with emphasis on marine model systems and applications, but which also provided fundamental insights into the control of infectious biofilms on biomedical devices. We used different methods (mechanical stretching, electrical-actuation and pneumatic-actuation) to generate dynamic deformation of elastomer surfaces. Our initial studies showed that dynamic surface deformation methods are effective in detaching laboratory grown bacterial biofilms and barnacles. Further systematic studies revealed that a threshold critical surface strain is required to debond a biofilm from the surface, and this critical strain is dependent on the biofilm mechanical properties including adhesion energy, thickness and modulus. To test the dynamic surface deformation approach in natural environment, we conducted field studies (at Beaufort, NC) in natural seawater using pneumatic-actuation of silicone elastomer. The field studies also confirmed that a critical substrate strain is needed to detach natural biofilm accumulated in seawater. Additionally, the results from the field studies suggested that substrate modulus also affect the critical strain needed to debond biofilms. To sum up, both the laboratory and the field studies proved that dynamic surface deformation approach can effectively detach various biofilms and barnacles, and therefore offers a non-toxic and environmental friendly approach for biofouling management.

Deformable elastomer systems used in our studies are easy to fabricate and can be used as complementary approach for existing commercial strategies for biofouling control. To this end, we aimed towards developed proactive multifunctional surfaces and proposed two different approaches: (i) modification of elastomers with antifouling polymers to produce multifunctional, and (ii) incorporation of silicone-oil additives into the elastomer to enhance fouling-release performance.

In approach (i), we modified poly(vinylmethylsiloxane) elastomer surfaces with zwitterionic polymers using thiol-ene click chemistry and controlled free radical polymerization. These surfaces exhibited both fouling resistance and triggered fouling-release functionalities. The zwitterionic polymers exhibited fouling resistance over short-term (∼hours) exposure to bacteria and barnacle cyprids. The biofilms that eventually accumulated over prolonged-exposure (∼days) were easily detached by applying mechanical strain to the elastomer substrate. In approach (ii), we incorporated silicone-oil additives in deformable elastomer and studied synergistic effect of silicone-oils and surface strain on barnacle detachment. We hypothesized that incorporation of silicone-oil additive reduces the amount of surface strain needed to detach barnacles. Our experimental results supported the above hypothesis and suggested that surface-action of silicone-oils plays a major role in decreasing the strain needed to detach barnacles. Further, we also examined the effect of change in substrate modulus and showed that stiffer substrates require lower amount of strain to detach barnacles.

In summary, this study shows that (1) dynamic surface deformation can be used as an effective, environmental friendly approach for biofouling control (2) stretchable elastomer surfaces modified with anti-fouling polymers provides a pro-active, dual-mode approach for biofouling control, and (3) incorporation of silicone-oils additives into stretchable elastomers improves the fouling-release performance of dynamic surface deformation technology. Dynamic surface deformation by itself and as a supplementary approach can be utilized biofouling management in biomedical, industrial and marine applications.

Visualization and prediction of spatial deformation using thin-plate splines in the context of scoliosis

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Simulating Granite Emplacement and Deformation with Centrifuge Analogue Modelling

The Greater Himalayan leucogranites are a discontinuous suite of intrusions emplaced in a thickened crust during the Miocene southward ductile extrusion of the Himalayan metamorphic core. Melt-induced weakening is thought to have played a critical role in strain localization that facilitated the extrusion. Recent advancements in centrifuge analogue modelling techniques allow for the replication of a broader range of crustal deformation behaviors, enhancing our understanding of large hot orogens. Polydimethylsiloxane (PDMS) is commonly used in centrifuge experiments to model weak melt zones. Difficulties in handling PDMS had, until now, limited its emplacement in models prior to any deformation. A new modelling technique has been developed where PDMS is emplaced into models that have been subjected to some shortening. This technique aims to better understand the effects of melt on strain localization and potential decoupling between structural levels within an evolving orogenic system. Models are subjected to an early stage of shortening, followed by the introduction of PDMS, and then a final stage of shortening. Theoretical percentages of partial melt and their effect on rock strength are considered when adding a specific percentage of PDMS in each model. Due to the limited size of the models, only PDMS sheets of 3 mm thickness were used, which varied in length and width. Within undeformed packages, minimal surface and internal deformation occurred when PDMS is emplaced in the lower layer of the model, showing a vertical volume increase of ~20% within the package; whereas the emplacement of PDMS into the middle layer showed internal dragging of the middle laminations into the lower layer and a vertical volume increase ~30%. Emplacement of PDMS results in ~7% shortening for undeformed and deformed models. Deformed models undergo ~20% additional shortening after two rounds of deformation. Strain localization and decoupling between units occur in deformed models where the degree of deformation changes based on the amount of partial melt present. Surface deformation visible by the formation of a bulge, mode 1 extension cracks and varying surface strain ellipses varies depending if PDMS is present. Better control during emplacement is exhibited when PDMS is added into cooler models, resulting in reduced internal deformation within the middle layer.