Generation of interface for an Allen-Cahn equation with nonlinear diffusion

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property

Effects of Synaptic and Myelin Plasticity on Learning in a Network of Kuramoto Phase Oscillators

Models of learning typically focus on synaptic plasticity. However, learning is the result of both synaptic and myelin plasticity. Specifically, synaptic changes often co-occur and interact with myelin changes, leading to complex dynamic interactions between these processes. Here, we investigate the implications of these interactions for the coupling behavior of a system of Kuramoto oscillators. To that end, we construct a fully connected, one-dimensional ring network of phase oscillators whose coupling strength (reflecting synaptic strength) as well as conduction velocity (reflecting myelination) are each regulated by a Hebbian learning rule. We evaluate the behavior of the system in terms of structural (pairwise connection strength and conduction velocity) and functional connectivity (local and global synchronization behavior). We find that for conditions in which a system limited to synaptic plasticity develops two distinct clusters both structurally and functionally, additional adaptive myelination allows for functional communication across these structural clusters. Hence, dynamic conduction velocity permits the functional integration of structurally segregated clusters. Our results confirm that network states following learning may be different when myelin plasticity is considered in addition to synaptic plasticity, pointing towards the relevance of integrating both factors in computational models of learning.Comment: 39 pages, 15 figures This work is submitted in Chaos: An Interdisciplinary Journal of Nonlinear Scienc

Synthesis and characterization of p-n junction ternary mixed oxides for photocatalytic coprocessing of CO2 and H2O

In the present paper, we report the synthesis and characterization of both binary (Cu2 O, Fe2 O3, and In2 O3 ) and ternary (Cu2 O-Fe2 O3 and Cu2 O-In2 O3 ) transition metal mixed-oxides that may find application as photocatalysts for solar driven CO2 conversion into energy rich species. Two different preparation techniques (High Energy Milling (HEM) and Co-Precipitation (CP)) are compared and materials properties are studied by means of a variety of characterization and analytical techniques UV-Visible Diffuse Reflectance Spectroscopy (UV-VIS DRS), X-ray Photoelectron Spectroscopy (XPS), X-Ray Diffraction (XRD), Transmission Electron Microscopy (TEM), and Energy Dispersive X-Ray spectrometry (EDX). Appropriate data elaboration methods are used to extract materials bandgap for Cu2 O@Fe2 O3 and Cu2 O@In2 O3 prepared by HEM and CP, and foresee whether the newly prepared semiconductor mixed oxides pairs are useful for application in CO2-H2 O coprocessing. The experimental results show that the synthetic technique influences the photoactivity of the materials that can correctly be foreseen on the basis of bandgap experimentally derived. Of the mixed oxides prepared and described in this work, only Cu2 O@In2 O3 shows positive results in CO2-H2 O photo-co-processing. Preliminary results show that the composition and synthetic methodologies of mixed-oxides, the reactor geometry, the way of dispersing the photocatalyst sample, play a key role in the light driven reaction of CO2 –H2 O. This work is a rare case of full characterization of photo-materials, using UV-Visible DRS, XPS, XRD, TEM, EDX for the surface and bulk analytical characterization. Surface composition may not be the same of the bulk composition and plays a key role in photocatalysts behavior. We show that a full material knowledge is necessary for the correct forecast of their photocatalytic behavior, inferred from experimentally determined bandgaps

Comparative life cycle assessment study on environmental impact of oil production from micro-algae and terrestrial oilseed crops

In this study the LCA methodology is applied in order to satisfy two goals: i) to evaluate the hot spots in site-specific production chain of biodiesel from terrestrial and micro-algae feedstock; ii) to compare quantitatively, utilizing primary data, the impacts of the first generation in respect to the third generation bio-fuels. Results show that micro-algae are neither competitive yet with traditional oil crops nor with fossil fuel. The use of renewable technologies as photovoltaics and biogas self production might increase the competitiveness of micro-algae oil. Further investigations are however necessary to optimize their production chain and to increase the added value of co-products

Opto‐Electronic Characterization of Photocatalysts Based on p,n‐Junction Ternary and Quaternary Mixed Oxides Semiconductors (Cu2O‐In2O3 and Cu2O‐In2O3‐TiO2)

Semiconductor materials are the basis of electronic devices employed in the communication and media industry. In the present work, we report the synthesis and characterization of mixed metal oxides (MOs) as p,n‐junction photocatalysts, and demonstrate the correlation between the preparation technique and the properties of the materials. Solid‐state UV-visible diffuse reflectance spectroscopy (UV‐VIS DRS) allowed for the determination of the light absorption properties and the optical energy gap. X‐ray photoelectron spectroscopy (XPS) allowed for the determination of the surface speciation and composition and for the determination of the valence band edge. The opto‐electronic behavior was evaluated measuring the photocurrent generated after absorption of chopped visible light in a 3‐electrode cell. Scanning electron microscopy (SEM) measurements allowed for auxiliary characterization of size and morphology, showing the formation of composites for the ternary Cu2O‐In2O3 p,n‐mixed oxide, and even more for the quaternary Cu2O‐In2O3‐TiO2 MO. Light absorption spectra and photocurrent‐time curves mainly depend upon the composition of MOs, while the optical energy gap and defective absorption tail are closely related to the preparation methodology, time and thermal treatment. Qualitative electronic band structures of semiconductors are also presented

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

Departures from isotropy: the kinematics of a larval snail in response to food

Author Posting. © Company of Biologists, 2020. This article is posted here by permission of Company of Biologists for personal use, not for redistribution. The definitive version was published in Journal of Experimental Biology 224(2), (2020): jeb.239178, https://doi.org/10.1242/jeb.239178.The swimming behavior of invertebrate larvae can affect their dispersal, survival and settlement in the ocean. Modeling this behavior accurately poses unique challenges as behavior is controlled by both physiology and environmental cues. Some larvae use cilia to both swim and create feeding currents, resulting in potential trade-offs between the two functions. Food availability is naturally patchy and often occurs in shallow horizontal layers in the ocean. Also, larval swimming motions generally differ in the horizontal and vertical directions. In order to investigate behavioral response to food by ciliated larvae, we measured their behavioral anisotropy by quantifying deviations from a model based on isotropic diffusion. We hypothesized that larvae would increase horizontal swimming and decrease vertical swimming after encountering food, which could lead to aggregation at food layers. We considered Crepidula fornicata larvae, which are specifically of interest as they exhibit unsteady and variable swimming behaviors that are difficult to categorize. We tracked the larvae in still water with and without food, with a portion of the larvae starved beforehand. On average, larvae in the presence of food were observed higher in the water column, with higher swimming speeds and higher horizontal swimming velocities when compared with larvae without food. Starved larvae also exhibited higher vertical velocities in food, suggesting no aggregation behavior. Although most treatments showed strong anisotropy in larval behavior, we found that starved larvae without food exhibited approximately isotropic kinematics, indicating that behavioral anisotropy can vary with environmental history and conditions to enhance foraging success or mitigate food-poor environments.M.H.D. and K.S.M.-K. were supported by postdoctoral scholarships from Woods Hole Oceanographic Institution, and B.T. was supported by a WHOI Summer Student Fellowship. This work was also supported by National Science Foundation grant OCE-0850419

Time-Frequency Signatures of Electronic Coherence of Colloidal CdSe Quantum Dot Dimer Assemblies Probed at Room Temperature by Two-Dimensional Electronic Spectroscopy

Electronic coherence signatures can be directly identified in the time-frequency maps measured in two-dimensional electronic spectroscopy (2DES). Here, we demonstrate the theory and discuss the advantages of this approach via the detailed application to the fast-femtosecond beatings of a wide variety of electronic coherences in ensemble dimers of quantum dots (QDs), assembled from QDs of 3 nm in diameter, with 8% size dispersion in diameter. The observed and computed results can be consistently characterized directly in the time-frequency domain by probing the polarization in the 2DES setup. The experimental and computed time-frequency maps are found in very good agreement, and several electronic coherences are characterized at room temperature in solution, before the extensive dephasing due to the size dispersion begins. As compared to the frequency-frequency maps that are commonly used in 2DES, the time-frequency maps allow exploiting electronic coherences without additional post-processing and with fewer 2DES measurements. Towards quantum technology applications, we also report on the modeling of the time-frequency photocurrent response of these electronic coherences, which paves the way to integrating QD devices with classical architectures, thereby enhancing the quantum advantage of such technologies for parallel information processing at room temperature

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis

In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We show the existence of an exponential attractor and, hence, of a finite-dimensional global attractor under certain 'balance conditions' on the order of the degeneracy and the growth of the chemotactic function