Flow Through Isotropic Granular (Non Consolidated) Porous Media

A generalization of the Navier-Stokes equations, proposed by Prieur du Plessis and Masliyah to model laminar flow through a rigid isotropic granular (non consolidated) porous medium of spatially varying permeability, is analyzed. Results concerning existence and regularity of solutions, similar to the ones holding the classical Navier-Stokes equations, are proved

Global Solutions Of A Model Of Phase Transitions For Dissipative Thermoviscoelastic Materials

We analyze a highly nonlinear system of partial differential equations that may be seen as a model for solidification or melting of certain viscoelastic materials subject to thermal effects; under the assumption that solid parts of the material may support damped vibrations. Phase change is controlled by a phase field equation with a potential including barriers at the pure solid and pure liquid states. The present system is closely related to a model analyzed by Rocca and Rossi [23]. They proved the existence of local in time solutions (global in the one dimensional case) assuming values just in the mushy zone, and thus such local solutions do not allow regions of pure solid or pure liquid states, except in the special one-dimensional case where pure liquid state is also allowed. By including a suitable dissipation in the previous model and assuming constant latent heat, in this work we are able to prove global in time existence even for solutions that may touch the potential barriers; that is, they allow regions with pure solid or pure liquid. © 2013 Texas State University - San Marcos.2013Adamsl, R., (1975) Sobolev Spaces, , Acad. PressBarbu, V., (1976) Nonlinear Semigroups and Differential Equations in Banach Epaces, , Noordhoff International Publishing, LeidenBonetti, E., Bonfanti, G., Existence and uniqueness of the solution to a 3D thermoviscoelastic system (2003) Electron. J. Differential Equations, 2003 (50), p. 15. , (electronic)Bonetti, E., Bonfanti, G., Asymptotic analysis for vanishing acceleration in a thermoviscoelas-tic system (2005) Abstr. Appl. Anal., 2005 (2), pp. 105-120Bonetti, E., Bonfanti, G., Well-posedness results for a model of damage in thermovis-coelastic materials (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire, , doi: 10.1016/ j. anihpc.2007.05.009Bonetti, E., Schimperna, G., Local existence to Frémond's model for damaging in elastic materials (2004) Contin. Mech. Thermodyn., 16, pp. 319-335Bonetti, E., Schimperna, G., Segatti, E., On a doubly nonlinear model for the evolution of damaging in viscoelastic materials (2005) J. Differential Equations, 218, pp. 91-116Bonfanti, G., Frémond, M., Luterotti, L., Global solution to a nonlinear system for irreversible phase changes (2000) Adv. Math. Sci. Appl., 10, pp. 1-24Brezis, H., Opérateurs Maximaux Monotones et Sémi-groupes de Contractions dans les Es-paces de Hilbert (1973) North-Holland Math. Stud., 5. , North-Holland Publishing Co./American Elsevier Publishing Co., Inc., Amsterdam, London/New YorkBrézis, H., Mironescu, P., Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces (2001) J. Evolution Equations, 1 (4), pp. 387-404Ciarlet, P., Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity (1988) Stud. Math. Appl., 20. , North-Holland Publishing Co., AmsterdamColli, P., Laurençot, P., Weak solutions to the Penrose-Fife phase field model for a class of admissible heat ux laws (1998) Phys. D, 111, pp. 311-334Frémond, M., (2002) Non-smooth Thermomechanics, , Springer, BerlinGermain, P., (1973) Cours de méchanique des milieux continus, , Tome I: Théorie générale, Masson et Cie, Éditeurs, ParisHoffman, K.H., Jiang, L., Optimal control of a phase field model for solidification (1992) Numer. Funct. Anal. Optimiz., 13 (1-2), pp. 11-27Kuttler, K.L., Quasistatic evolution of damage in an elastic-viscoplastic material (2005) Electron. J. Differential Equations 2005, 147, p. 25. , (electronic)Ladyzhenskaya, O.A., Ural'tseva, N.N., (1968) Linear and Quasilinear Elliptic Equations, , Academic Press, New YorkLadyzhenskaya, O.A., Solonnikov, V., Ural'tseva, N.N., (1968) Linear and Quasilinear Equations of Parabolic Type, , American Mathematical SocietyMoroşanu, C., Motreanu, D., A generalized phase field system (1999) Journal of Math. Analysis and Applic., 237, pp. 515-540Nečas, J., Les méthodes directes en théorie des équations elliptiques (1967), Masson et Cie, Éditeurs, ParisRocca, E., Rossi, R., Analysis of a nonlinear degenerating PDE system for phase transitions in thermoviscoelastic materials (2008) J. Differential Equations, 245, pp. 3327-3375Rocca, E., Rossi, R., Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials (2008) Appl. Math., 53 (5), pp. 485-520Rocca, E., Rossi, R., (2012) A degenerating PDE system for phase transitions and damage, p. 153. , preprint arXiv:1205.3578v1Simon, J., Compact sets in the space Lp(0T;B) (1987) Ann. Mat. Pura Appl., 146 (4), pp. 65-96Stefanelli, U., (2003) Models of phase change with microscopic movements, , PhD thesis, University of PaviaTemam, R., Navier-Stokes Equations: Theory and Numerical Analysis (1984) Stud. Math. Appl., 2. , third ed. North-Holland Publishing Co., Amsterda

Existence And Uniqueness Of Stationary Solutions To Bioconvective Flow Equations

We analyze a system of nonlinear partial differential equations modeling the stationary flow induced by the upward swimming of certain microorganisms in a fluid. We consider the realistic case in which the effective viscosity of the fluid depends on the concentration of such microorganisms. Under certain conditions, we prove the existence and uniqueness of solutions for such generalized bioconvective flow equations. © 2013 Texas State University - San Marcos.2013Adams, R.A., (1975) Sobolev Spaces, , Academic Press, New YorkBrezis, H., (1987) Analyse Fonctionnelle-théorie Et Applications, 2 Tirage, , MassonCliment-Ezquerra, B., Friz, L., Rojas-Meda, M.A., Time-reproductive solutions for a bioconvective flow Applicata, , Annali di Matematica Pura ed, Press, DOI 10.1007/s10231-011-0245-7Kan-On, Y., Narukawa, K., Teramoto, Y., On the equations of bioconvective flow (1992) J. Math. Kyoto Univ. (JMKYAZ), 32 (1)Levandowsky, M., Childress, W.S., Hunter, S.H., Spiegel, E.A., A mathematical model of pattern formation by swimming microorganisms, J (1975) Protozoology, 22Lorca, S., Boldrini, J.L., Stationary solutions for generalized Boussinesq models, J (1996) Differential Equations, 2, p. 124Lorca, S., Boldrini, J.L., (1999) The Initial Value Problem For a Generalized Boussinesq Model, Nonlinear Analysis: Theory, Methods and Applications, 36 (4)Moribe, Y., (1973) On the Bioconvection of Tetrahymena Pyriformis, , Master's Thesis, Osaka UniversityRionero, S., Mulone, G., Existence and Uniqueness Theorems for a Steady Thermo-Diffusive Mixture in a Mixed Problem (1988) Nonlinear Analysis, TMA, Col, 5, p. 12Solonnikov, V., Scadilov, V., On a boundary value problem for a stationary system of Navier-Stokes equations (1973) Proc. Steklov Inst. Math, p. 125Temam, R., (1979) Navier-Stokes Equations-Theory and Numerical Analysis, , (revised edition), North-Holland Publ., Comp., Amsterda

Supramolecular interactions in clusters of polar and polarizable molecules

We present a model for molecular materials made up of polar and polarizable molecular units. A simple two state model is adopted for each molecular site and only classical intermolecular interactions are accounted for, neglecting any intermolecular overlap. The complex and interesting physics driven by interactions among polar and polarizable molecules becomes fairly transparent in the adopted model. Collective effects are recognized in the large variation of the molecular polarity with supramolecular interactions, and cooperative behavior shows up with the appearance, in attractive lattices, of discontinuous charge crossovers. The mean-field approximation proves fairly accurate in the description of the gs properties of MM, including static linear and non-linear optical susceptibilities, apart from the region in the close proximity of the discontinuous charge crossover. Sizeable deviations from the excitonic description are recognized both in the excitation spectrum and in linear and non-linear optical responses. New and interesting phenomena are recognized near the discontinuous charge crossover for non-centrosymmetric clusters, where the primary photoexcitation event corresponds to a multielectron transfer.Comment: 14 pages, including 11 figure

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time, and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space. While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes, vast areas of the tropics remain understudied. In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity, but it remains among the least known forests in America and is often underrepresented in biodiversity databases. To worsen this situation, human-induced modifications may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge, it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost