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Search results for: GENERALIZED CONTINUUM MECHANICS
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Computational methods for calculation of binding free energy for ligand-receptor complexes
PublicationAccurate description of the molecular complexes energetic influence is required for understanding of many biological functions carried out by proteins. Therefore, estimation of binding free energy for ligand-receptor complexes is of highest importance for structure-based ligand design and drug discovery approaches.Experimental methods of determination of difference in Gibbs'es free energy have many limitations. Thus, computational...
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Duhem and Natanson: Two Mathematical Approaches to Thermodynamics
PublicationIn this article, the previously unrecognized contributions of Pierre Duhem and Ladislavus Natanson in thermodynamics are shown. The mathematical remodelling of a few of their principal ideas is taken into consideration, despite being neglected in the literature. To emphasize these ideas in an appropriate epistemological order, it would be crucial to first revalue and reconstruct some underrepresented parts of the proceedings process...
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Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells
PublicationWe formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected,...
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Scalar and Vector acoustic fields and sources: a new look
PublicationA study of fundamental problems of the wavefields that are the reaction of fluid continuum on two kinds of primary actions in fluid, then on two kinds of elementary point sources, is presented in this paper, based on the assumption of the physical duality of linear fluid mechanics and the formal symmetry of mathematical description. The two fundamental wavefields generated in fluid by physical point sources are discussed in detail,...
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On coertia and inertia in aspects of Natanson’s nonlinear extended thermodynamics
PublicationIn this article, the previously underrepresented contributions of Natanson to the field of thermodynamics have been presented. In order to identify a source of irreversibility at Nature, Natanson introduced the concept of Coertia, which is similar to inertia. Natanson’s Coertia is a fundamental property of space that is responsible for every irreversible phenomena in matter, as well as in the electromagnetic and gravitational fields....
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Strongly anisotropic surface elasticity and antiplane surface waves
PublicationWithin the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic...
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A constitutive law for concrete with smooth transition from continuous into discontinuous cracks’ description
PublicationPaper presents a constitutive model for concrete that combines a continuous and discontinuous crack’s description to simulate the concrete under tensile dominated loads. In a continuum regime, two different constitutive laws were used. First, a plasticity model with the Rankine failure criterion and an associated flow rule was used. Second, a constitutive law based on isotropic damage mechanics was formulated. Both model alternatives...
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Marek Czachor prof. dr hab.
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Structured deformation of granular material in the state of active earth pressure
PublicationThe paper focuses on the ability of granular materials to undergo structured deformation by analysing the data from the retaining wall model tests and discrete element simulations. The structured deformation means the movement of a granular material which produces a stable, regular pattern of multiple shear bands. The paper's primary purpose is to study this kind of deformation for the selected data representing the state of active...
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INNOVATIVE THERMODYNAMICAL CYCLES BASED ON ENHANCEMENT MASS, MOMENTUM, ENTROPY AND ELECTRICITY TRANSPORT DUE TO SLIP, MOBILITY, TRANSPIRATION, ENTROPY AND ELECTRIC JUMPS AS WELL AS OTHER NANO-FLOWS PHENOMENA
PublicationIn our work, a further development of the authors model of thermo-chemical flow of fuel, air, oxygen, steam water, species, ionic and electron currents within nano channels and nano-structures of novel devices is presented. Different transport enhancement models are taken into account -among them the most important are: the velocity slip connected with complex external friction, the Darcy mobility and the Reynolds transpiration....
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On time-dependent nonlinear dynamic response of micro-elastic solids
PublicationA new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium....
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Static electric and magnetic multipole susceptibilities for Dirac one-electron atoms in the ground state
PublicationWe present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range $1\leq Z\leq137$. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities $\alpha_{\mathrm{E}L\to\mathrm{E}L}$ and magnetizabilities (magnetic susceptibilities) $\chi_{\mathrm{M}L\to\mathrm{M}L}$...
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Continuum models for pantographic blocks with second gradient energies which are incomplete
PublicationWe postulate a deformation energy for describing the mechanical behavior of so called pantographic blocks, that is bodies constituted by stacking of layers of pantographic sheets. We remark that the pantographic effect is limited in the plane of pantographic sheets and therefore only the second derivatives of transverse displacements along the pantographic fibers appear in the chosen deformation energy. We use this novel energy...
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Nonlocal Models of Plates and Shells with Applications in Micro- and Nanomechanics
PublicationNowadays, the use of small-scale structures in micro/nanomachines has become more and more widespread. The most important applications of such small-sized parts are in micro-electro-mechanical systems (MEMS) as well as nano-electro-mechanical systems (NEMS) as actuators, sensors, energy harvesters. For example, nanosensors are nanoscale devices that measure physical quantities and convert these to signals that can be detected and...
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On Invariants of Fluid Mechanics Tensors
PublicationThis paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.
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Unifying Aspects of Generalized Calculus
PublicationNon-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.
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Generalized adaptive notch smoothing revisited
PublicationThe problem of identification of quasi-periodically varying dynamic systems is considered. This problem can be solved using generalized adaptive notch filtering (GANF) algorithms. It is shown that the accuracy of parameter estimates can be significantly increased if the results obtained from GANF are further processed using a cascade of appropriately designed filters. The resulting generalized adaptive notch smoothing (GANS) algorithm...
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Some Introductory and Historical Remarks on Mechanics of Microstructured Materials
PublicationHere we present few remarks on the development of the models of microstuctured media and the generalized continua.
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On mechanics of piezocomposite shell structures
PublicationThis study presents an original and novel investigation into the mechanics of piezo-flexo-magneto-elastic nanocomposite doubly-curved shells (PFMDCSs) and the ability to detect the lower and higher levels of electro-magnetic fields. In this context, by utilizing the first-order shear deformation shell model, stresses and strains are acquired. By imposing Hamilton's principle and the von Kármán approach, the governing equations...
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Continuum orbitals in low energy scattering of electrons from Ar, Kr, Xe, Rn and Og atoms
Open Research DataThe dataset includes relativistic continuum electron wave functions (continuum orbitals, continuum spinors) for elastic scattering of electrons from Argon (Ar), Krypton (Kr), Xenon (Xe), Radon (Rn) and Oganesson (Og) atoms, calculated using the Multiconfiguration Dirac-Hartree-Fock method (MCDHF), at very low electron energies (0.0001 - 0.001 eV). Only...
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Polynomial Chaos Expansion in Bio- and Structural Mechanics
PublicationThis thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair...
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Polynomial Chaos Expansion in Bio-and Structural Mechanics
PublicationThis monograph presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the...
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Optics Continuum
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Generalized Dold sequences on partially-ordered sets
PublicationDold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...
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Acceleration waves in the nonlinear micromorphic continuum
PublicationWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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English for Engineering Mechanics
e-Learning CoursesThe activity of structural mechanics students' community FOREVER YOUNG aimed at improving practical skills in technical English
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Applied Mechanics and Materials
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublicationIn this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.
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Archives of Hydro-Engineering and Environmental Mechanics
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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A simple way of increasing estimation accuracy of generalized adaptive notch filters
PublicationGeneralized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. It is shown that frequency biases, which arisein generalized adaptive notch filtering algorithms, can be significantly reduced by incorporating in the adaptive loop an appropriately chosen decision delay. The resulting performance...
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Generalized adaptive notch smoothers for real-valued signals and systems
PublicationSystems with quasi-periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters (GANFs). GANF algorithms can be considered an extension, to the system case, of classical adaptive notch filters (ANFs). We show that estimation accuracy of the existing algorithms, as well as their robustness to the choice of design parameters, can be considerably improved by means of compensating...
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Theoretical calculation of pKas of phosphoric (V) acidin the polarisable continuum and cluster-continuum models
PublicationW pracy oceniono dokładność modelu polaryzowalnego kontinuum (PCM) i mieszanego modelu klaster-kontinuum do przewidywania wartości trzech kolejnych stałych dysocjacji kwasu fosforowego (V). Obliczenia PCM na poziomie MP2/6-31+G(d,p) odtwarzają wartość pierwszego pKa z rozsądną niepewnością, jednak wartości kolejnych pKa obarczone są bardzo dużym błędem, nawet po podniesieniu poziomu teorii do metody zespolonej G3B3. Dopiero obliczenia...
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ENGINEERING FRACTURE MECHANICS
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Generalized temperature dependence model for anammox process kinetics
PublicationTemperature is a key operational factor influencing the anammox process kinetics. In particular, at temperatures below 15 °C, the specific anammox activity (SAA) considerably decreases. This study aimed to describe the temperature dependence of the anammox process kinetics in the temperature range from 10 to 55 °C, including the specific characteristics of“cold anammox”. The commonly used Arrhenius and extended and modifiedRatkowsky...
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Quasi-solutions for generalized second order differential equations with deviating arguments
PublicationThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.
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Automated microwave planar filter design with generalized Chebyshev characteristics.
PublicationIn this paper a technique of automatization of design of microwave filters with generalized Chebyshev characteristics is presented. A full wave electromagnetic simulator linked with the Matlab computing environment is used to ensure a rigorous numerical analysis while at the same time allowing automatization. To decrease time of optimization and overall design process, the Cauchy interpolation technique was used. An automated design...
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Continuum wave functions for estimating the electric dipole moment: Calculation based on a multiconfiguration Dirac-Hartree-Fock approximation
PublicationThe multiconfiguration Dirac-Hartree-Fock method is employed to calculate the continuum electron wave functions, which are then used to estimate their contribution to the atomic electric dipole moment (EDM) of 129Xe. The EDM arises from (P,T)-odd electron-nucleon tensor-pseudotensor and pseudoscalar-scalar interactions, the nuclear Schiff moment, the interaction of the electron electric dipole moment with nuclear magnetic moments,...
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Probing the structure of quantum mechanics
PublicationWstęp do problemów dotyczących struktury mechaniki kwantowej, a w szczegółności związanych z jej nieliniowością, nielokalnością, a także problemami aks-jomatyzacji i wykorzystaniem zjawisk kwantowych do budowy komuterów.
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Multistage generalized adaptive notch filter with improved accuracy
PublicationGeneralized adaptive notch filters (GANFs) are estimators of coefficients of quasi-periodically time-varying systems. Current state of the art GANFs can deliver highly accurate estimates of system variations’ frequency, but underperform in terms of accuracy of the coefficient estimates. The paper proposes a novel multistage GANF with accuracy improved in this aspect. The processing pipeline consists of three stages. The preliminary...
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Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems
PublicationGeneralized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can...
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A self-optimization mechanism for generalized adaptive notch smoother
PublicationTracking of nonstationary narrowband signals is often accomplished using algorithms called adaptive notch filters (ANFs). Generalized adaptive notch smoothers (GANSs) extend the concepts of adaptive notch filtering in two directions. Firstly, they are designed to estimate coefficients of nonstationary quasi-periodic systems, rather than signals. Secondly, they employ noncausal processing, which greatly improves their accuracy and...
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Generalized adaptive comb filter with improved accuracy and robustness properties
PublicationGeneralized adaptive comb lters can be used to identify/track parameters of quasi-periodically varying systems.In a special, signal case they reduce down to adaptive comblters, applied to elimination or extraction of nonstationarymulti-harmonic signals buried in noise. We proposea new algorithm which combines, in an adaptive way, resultsyielded by several, simultaneously working generalizedadaptive comb lters. Due to its highly...
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Journal of Theoretical and Applied Mechanics
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Jacek Tejchman prof. dr hab. inż.
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Application of fracture mechanics for energetic effects predictions while wood sawing
PublicationIn the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, cutting forces (power) could be considered from a point of view of modern fracture mechanics. Cutting forces may be employed to determine not only toughness...
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CUTTING POWER FORECASTING WHILE WOOD SAWING: FRACTURE MECHANICS APPROACH AND AXELSSON’S MODEL COMPARISON
PublicationIn the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, cutting forces (power) could be considered from a point of view of modern fracture mechanics. Another way is to forecast cutting power consumption on...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublicationIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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Application of Fracture Mechanics for Energetic Effects Predictions While Wood Sawing
PublicationIn the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, cutting forces (or power - more interesting from energetic point of view) could be considered from a point of view of modern fracture mechanics. Cutting...