1,721,013 research outputs found
Su alcune questioni di Calcolo delle Variazioni: omogeneizzazione in domini perforati con condizioni di Neumann e rilassamento. (dottorando Cardone Giuseppe)
No full textDerivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers
Full text linkWe derive, through the deterministic homogenization theory in thin domains, a
new model consisting of Hele-Shaw equation with memory coupled with the
convective Cahn-Hilliard equation. The obtained system, which models in
particular tumor growth, is then analyzed and we prove its well-posedness in
dimension 2. To achieve our goal, we develop and use the new concept of
sigma-convergence in thin heterogeneous media, and we prove some regularity
results for the upscaled model.Comment: 52 page
Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation
Full text linkWe consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide Πl ε formed by the union of an infinite strip and a narrow box-shaped perturbation of size 2l×ε, where ε>0 is a small parameter. We prove the existence of the length parameter lk ε=πk+O(ε) with any k=1,2,3,. such that the waveguide Πlk ε ε supports a trapped mode with an eigenvalue λk ε=π2−4π4l2ε2+O(ε3) embedded into the continuous spectrum. This eigenvalue is unique in the segment [0,π2], and it is absent in the case l≠lk ε. The detection of this embedded eigenvalue is based on a criterion for trapped modes involving an artificial object, the augmented scattering matrix. The main difficulty is caused by the rather specific shape of the perturbed wall ∂Πl ε, namely a narrow rectangular bulge with corner points, and we discuss available generalizations for other piecewise smooth boundaries
Spectra of operator pencils with small -symmetric periodic perturbation
No full textWe study the spectrum of a quadratic operator pencil with a small -symmetric periodic potential and a fixed localized potential. We show that the continuous spectrum has a band structure with bands on the imaginary axis separated by usual gaps, while on the real axis, there are no gaps but at certain points, the bands bifurcate into small parabolas in the complex plane. We study the isolated eigenvalues converging to the continuous spectrum. We show that they can emerge only in the aforementioned gaps or in the vicinities of the small parabolas, at most two isolated eigenvalues in each case. We establish sufficient conditions for the existence and absence of such eigenvalues. In the case of the existence, we prove that these eigenvalues depend analytically on a small parameter and we find the leading terms of their Taylor expansions. It is shown that the mechanism of the eigenvalue emergence is different from that for small localized perturbations studied in many previous works
δ′-interaction as a limit of a thin Neumann waveguide with transversal window
No full textWe consider a waveguide-like domain consisting of two thin straight tubular domains connected through a tiny window. The perpendicular size of this waveguide is of order ε. Under the assumption that the window is appropriately scaled we prove that the Neumann Laplacian on this domain converges in (a kind of) norm resolvent sense as ε→0 to a one-dimensional Schrödinger operator corresponding to a δ′-interaction of a non-negative strength. We estimate the rate of this convergence, also we prove the convergence of spectra
Effect of feedstock demineralization on physico-chemical characteristics of arundo donax derived biochar
No full textSolid residue derived from thermochemical degradation of vegetal biomass, generally named biochar, is
currently under study for its potential agronomic value as soil amender and fertilizer. Feedstock pretreatments
aiming to a partial demineralization of the biomass could promote the development of char
porosity by inducing modifications of the chemical and physical characteristics of the feedstock. In the
present paper three different methods of feedstock demineralization have been applied on Arundo donax
samples. Steam assisted pyrolysis of raw and demineralized Arundo donax has been carried out in a
proper experimental apparatus up to 873 K, at pressure P=5×105
Pa and heating rate HR=5 K/min. A
comparison of the chemical and physical properties of produced chars and energetic content of gaseous
phase has been evaluated for its possible use as fuel to sustain biochar production itself
Thin elastic plates supported over small areas. II. Variational-asymptotic models
No full textAn asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area of one base with diameter of the same order as the plate thickness A three-dimensional boundary layer in the vicinity of the support is involved into the asymptotic form which is justified by means of the previously derived weighted inequality of Korn's type provides an error estimate with the bound . Ignoring this boundary layer effect reduces the precision order down to . A two-dimensional variational-asymptotic model of the plate is proposed within the theory of self-adjoint extensions of differential operators. The only characteristics of the boundary layer, namely the elastic logarithmic potential matrix of size , is involved into the model which however keeps the precision order in certain norms. Several formulations and applications of the model are discussed
Hemicellulose, cellulose and lignin interactions on Arundo donax steam assisted pyrolysis
No full textSlow Steam pyrolysis of Arundo donax is proposed as possible process for the recovery of a solid material suitable to be used as biochar. In view of the evaluation of the feasibility of such a process, products yields, surface area of char and energetic content of gaseous products needed to assist energetically the process are relevant data to be evaluated in dependence on process operating conditions and biomass characteristics. Biomass main components (hemicellulose, cellulose and lignin) contribute to a different extent to the determination of products yield and characteristics both for their own intrinsic chemical nature and for the onset of possible interactions due to their simultaneous presence in a real biomass. Moreover, it is known that inorganic elements present in the biomass can affect pyrolysis mechanisms and consequently products yields and characteristics. In the present paper the influence of inorganic species and of possible interactions between biomass main components on pyrolysis of A. donax has been studied. To this aim steam assisted pyrolysis tests have been carried out on a mixture of xylan, cellulose and lignin resembling the composition of A. donax canes in a proper experimental apparatus up to 873 K, at pressure P = 5 × 105 Pa and heating rate HR = 5 K/min. Products yields, gas releasing rate as function of the temperature, gas composition and specific internal surface of char have been compared to the data computed from the superposition of the results obtained for the single components and to the behavior of untreated and demineralized samples of A. donax canes processed in the same experimental apparatus in the same operating conditions. Results obtained from this study show that primary pyrolysis of holocellulose is affected by the presence of inorganic species that depress the devolatilization of heavier compounds in favor of cracking reactions determining a higher release of light compounds, CO2 and CO. Moreover, interactions between lignin and cellulose are relevant in operating conditions where mass transfer phenomena cannot be neglected. Interesting results have been obtained for the solid residue as for the development of its internal surface that seems to be reduced from both interactions between biomass components and presence of inorganic ions
Asymptotic analysis of an array of closely spaced absolutely conductive inclusions
Full text linkWe consider the conductivity problem in an array structure with
square closely spaced absolutely conductive inclusions of the high concentra-
tion, i.e. the concentration of inclusions is assumed to be close to 1. The
problem depends on two small parameters: ", the ratio of the period of the
micro-structure to the characteristic macroscopic size, and , the ratio of the
thickness of the strips of the array structure and the period of the micro-
structure. The complete asymptotic expansion of the solution to problem is
constructed and justified
Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes
No full textIn this paper, we study the asymptotic behaviour of solutions of a coupled system of par-
tial differential equations in a thin domain with oscillating boundary and varying order of
thickness. In such a thin domain, our model describes the solute concentration of two dif-
ferent biochemical species (metabolites). The coupling between the concentrations of the
metabolites is realized through reaction terms even nonlinear, appearing on the oscillating
upper wall. Moreover nonlinear reaction terms appear also in the thin domain. The reaction
catalyzed by the upper wall is simulated by a Robin-type boundary condition depending on a
small parameter ε. Hence, taking into account that α > 1 and β > 0, we analyze the coupled
system by comparing the magnitude of the reaction coefficient ε β on the upper boundary
with the compression order of our thin domain, which can be ε or ε α , depending on the sub-
regions with different order of thickness. Comparing the exponents 1, α and β, we obtain
different cases for the limit problem which could appear coupled or uncoupled and allow us
to identify the effects of the geometry and the physical process on the problem. Moreover it
arises a critical value, i.e. β = α − 2, leading the reaction effects entering in the diffusion
matri
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