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Search results for: weak solutions
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
PublicationWe consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublicationWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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Structured populations with diffusion and Feller conditions
PublicationWe prove a weak maximum principle for structured population models with dynamic boundary conditions. We establish existence and positivity of solutions of these models and investigate the asymptotic behaviour of solutions. In particular, we analyse so called size profile.
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublicationIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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Interactions in aqueous solutions of K-peptide and DMSO – spectroscopic and calorimetric studies
PublicationIntroduction K-peptide (GILQINSRW) – short 9 amino acid fragment of the hen egg white lysozyme has the ability to form amyloid structures. Dimethyl sulfoxide (DMSO) is an osmolyte which can alter this ability. Our goal was to get an insight into the mechanism of Kpeptide-DMSO interactions in aqueous solutions. Such a knowledge can be helpful to understand processes leading to various neurodegenerative diseases. Methods ATR-FTIR...
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
PublicationIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class...
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The hydration of selected biologically relevant molecules – the temperature effect on apparent molar volume and compression
PublicationThe densities and sound velocities at T = (288.15, 293.15, 298.15, 303.15 and 308.15) K were measured for aqueous solutions of glycine, trimethylamine-N-oxide, taurine and N-methylacetamide. From these data, the apparent molar volumes, V the apparent molar isentropic compressions, KS,, and the Passynski hydration numbers of solutes were determined. The concentration dependencies of the calculated quantities, their limiting values...
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Organic solvents aggregating and shaping structural folding of protein, a case study of the protease enzyme
PublicationLow solubility of reactants or products in aqueous solutions can result in the enzymatic catalytic reactions that can occur in non-aqueous solutions. In current study we investigated aqueous solutions containing different organic solvents / deep eutectic solvents (DESs) that can influence the protease enzyme's activity, structural, and thermal stabilities. Retroviral aspartic protease enzyme is responsible for the cleavage of the...
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Anion–water interactions of weakly hydrated anions: molecular dynamics simulations of aqueous NaBF4 and NaPF6
PublicationIn aqueous ionic solutions, both the structure and the dynamics of water are altered dramatically with respect to the pure solvent. The emergence of novel experimental techniques makes these changes accessible to detailed investigations. At the same time, computational studies deliver unique possibilities for the interpretation of the experimental data at the molecular level. Here, using molecular dynamics simulations, we demonstrate...
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Value of Age Diversity – Declarations and Practice in Polish Organizations
PublicationThe present article relates to management of age diverse teams in organisations and enterprises located in Poland. Managing diversity is an active and conscious process leading not only to a lack of discriminatory conduct but above all to making full use of the potential of the team. The potential resulting from the diversity of knowledge, skills and experience. The diversity of the age of the team members is in fact a differentiation...
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Hydration of amino acids: FTIR spectra and molecular dynamics studies
PublicationThe hydration of selected amino acids, alanine, glycine, proline, valine, isoleucine and phenylalanine, has been studied in aqueous solutions by means of FTIR spectra of HDO isotopically diluted in H2O. The difference spectra procedure and the chemometric method have been applied to remove the contribution of bulk water and thus to separate the spectra of solute-affected HDO. To support interpretation of obtained spectral results,...
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Unique agreement of experimental and computational infrared spectroscopy: a case study of lithium bromide solvation in an important electrochemical solvent
PublicationInfrared (IR) spectroscopy is a widely used and invaluable tool in the studies of solvation phenomena in electrolyte solutions. Using state-of-the-art chemometric analysis of a spectral series measured in a concentration-dependent manner, the spectrum of the solute-affected solvent can be extracted, providing a detailed view of the structural and energetic states of the solvent molecules influenced by the solute. Concurrently,...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Open Research DataThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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Determination of changes in viscosity of chitosan solutions depending on shear rate.
Open Research DataThe rheological characteristics of chitosan solutions were based on viscosity measurements using a Brookfield viscometer, using LV SC4 - 25 spindles and shear rates from 4 to 53 s-1 (Fig. 1). Chitosan solutions with different molecular weights (low, medium and high) were prepared in concentrations from 1.5 to 3.0% in 0.5M acetic acid. The data allowed...
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Experimental Study of the Resistance to Influence of Aggressive Liquids on Lightweight Concrete
PublicationIn light of the scientific research, the corrosion of concrete structures is one of the main problems that may reduce their durability due to the negative impact of the natural environment. The paper analyzes the influence of the type of component on the selected properties of lightweight concrete subjected to the influence of aggressive liquids. Four concrete mixes were prepared with a granular aggregate made of foamed glass (GEGA)...