1. | Kiełczyński P., Direct Sturm–Liouville problem for surface Love waves propagating in layered viscoelastic waveguides, Applied Mathematical Modelling, ISSN: 0307-904X, DOI: 10.1016/j.apm.2017.09.013, Vol.53, pp.419-432, 2018Kiełczyński P., Direct Sturm–Liouville problem for surface Love waves propagating in layered viscoelastic waveguides, Applied Mathematical Modelling, ISSN: 0307-904X, DOI: 10.1016/j.apm.2017.09.013, Vol.53, pp.419-432, 2018Abstract: This paper presents theoretical model for shear-horizontal (SH) surface acoustic waves of the Love type propagating in lossy waveguides consisting of a lossy viscoelastic layer de- posited on a lossless elastic half-space. To this end, a direct Sturm–Liouville problem that describes Love waves propagation in the considered viscoelastic waveguides was formu- lated and solved, what constitutes a novel approach to the state-of-the-art. To facilitate the solution of the complex dispersion equation, the Author employed an original ap- proach that relies on the separation of its real and imaginary part. By separating the real and imaginary parts of the resulting complex dispersion equation for a complex wave vec- tor k = k 0 + j αof the Love wave, a system of two real nonlinear transcendental algebraic equations for k 0 and αhas been derived. The resulting set of two algebraic transcenden- tal equations was then solved numerically. Phase velocity v p and coefficient of attenuation αwere calculated as a function of the wave frequency f , thickness of the surface layer h and its viscosity η44 . Dispersion curves for Love waves propagating in lossy waveguides, with a lossy surface layer deposited on a lossless substrate, were compared to those cor- responding to Love surface waves propagating in lossless waveguides, i.e., with a lossless surface layer deposited on a lossless substrate. The results obtained in this paper are orig- inal and to some extent unexpected. Namely, it was found that: 1) the phase velocity v p of Love surface waves increases as a function of viscosity η44 of the lossy surface layer, and 2) the coefficient of attenuation αhas a maximum as a function of thickness h of the lossy surface layer. The results obtained in this paper are novel and can be applied in geo- physics, seismology and in the optimal design and development of viscosity sensors, bio and chemosensors. Keywords: Sturm–Liouville problem; Complex dispersion equation; Surface acoustic love waves; Eigenvalues; Elastic waves; Viscoelastic waveguides | |
2. | Dziekoński C., Dera W., Jarząbek D.M., Method for lateral force calibration in atomic force microscope using MEMS microforce sensor, ULTRAMICROSCOPY, ISSN: 0304-3991, DOI: 10.1016/j.ultramic.2017.06.012, Vol.182, pp.1-9, 2017Dziekoński C., Dera W., Jarząbek D.M., Method for lateral force calibration in atomic force microscope using MEMS microforce sensor, ULTRAMICROSCOPY, ISSN: 0304-3991, DOI: 10.1016/j.ultramic.2017.06.012, Vol.182, pp.1-9, 2017Abstract: In this paper we present a simple and direct method for the lateral force calibration constant determination. Our procedure does not require any knowledge about material or geometrical parameters of an investigated cantilever. We apply a commercially available microforce sensor with advanced electronics for direct measurement of the friction force applied by the cantilever's tip to a flat surface of the microforce sensor measuring beam. Due to the third law of dynamics, the friction force of the equal value tilts the AFM cantilever. Therefore, torsional (lateral force) signal is compared with the signal from the microforce sensor and the lateral force calibration constant is determined. The method is easy to perform and could be widely used for the lateral force calibration constant determination in many types of atomic force microscopes. Keywords: A precise and direct method for lateral force calibration, Inaccuracy equal to approximately 2%, Wedge method is proven to give inaccurate results | |
3. | Banach Z., Larecki W., Entropy-based mixed three-moment description of fermionic radiation transport in slab and spherical geometries, Kinetic and Related Models, ISSN: 1937-5093, DOI: 10.3934/krm.2017035, Vol.10, No.4, pp.879-900, 2017Banach Z., Larecki W., Entropy-based mixed three-moment description of fermionic radiation transport in slab and spherical geometries, Kinetic and Related Models, ISSN: 1937-5093, DOI: 10.3934/krm.2017035, Vol.10, No.4, pp.879-900, 2017Abstract: The mixed three-moment hydrodynamic description of fermionic radiation transport based on the Boltzmann entropy optimization procedure is considered for the case of one-dimensional flows. The conditions for realizability of the mixed three moments chosen as the energy density and two partial heat fluxes are established. The domain of admissible values of those moments is determined and the existence of the solution to the optimization problem is proved. Here, the standard approaches related to either the truncated Hausdorff or Markov moment problems do not apply because the non-negative fermionic distribution function, denoted f, must satisfy the inequality f _ 1 and, at the same time, there are three different intervals of integration in the integral formulae defining the mixed moments. The hydrodynamic equations are obtained in the form of the symmetric hyperbolic system for the Lagrange multipliers of the optimization problem with constraints. The potentials generating this system are explicitly determined as dilogarithm and trilogarithm functions of the Lagrange multipliers. The invertibility of the relation between moments and Lagrange multipliers is proved. However, the inverse relations cannot be determined in a closed analytic form. Using the H-theorem for the radiative transfer equation, it is shown that the derived system of hydrodynamic radiation equations has as a consequence an additional balance law with a non-negative source term. Keywords: Fermionic radiation, mixed moments, moment realizability domain, entropy optimization problem, symmetric hyperbolicity | |
4. | Jarząbek D.M., Milczarek M., Wojciechowski T., Dziekoński C., Chmielewski M., The effect of metal coatings on the interfacial bonding strength of ceramics to copper in sintered Cu-SiC composites, CERAMICS INTERNATIONAL, ISSN: 0272-8842, DOI: 10.1016/j.ceramint.2017.01.056, pp.1-9, 2017Jarząbek D.M., Milczarek M., Wojciechowski T., Dziekoński C., Chmielewski M., The effect of metal coatings on the interfacial bonding strength of ceramics to copper in sintered Cu-SiC composites, CERAMICS INTERNATIONAL, ISSN: 0272-8842, DOI: 10.1016/j.ceramint.2017.01.056, pp.1-9, 2017Abstract: Cu-SiC composites are very promising materials which have high thermal and electrical conductivity and may find many applications. Unfortunately, the main disadvantage of these materials is the dissolution of silicon in copper at elevated temperature, which significantly reduces their properties. In order to overcome this problem particles can be coated with a protective material before sintering. In this paper– the influence of three different metallic coatings on bonding strength were investigated. SiC particles were coated with tungsten, chromium or titanium. As reference a material with uncoated particles was prepared. The experiments were carried out with the use of microtensile tester. The highest increase in strength was observed in the case of chromium coating. On the other hand, the titanium coating, which was of very poor quality, decrease the bonding strength in comparison with uncoated particles. Furthermore, scanning electron and optical microscopes were used to determine the mechanism of debonding. Keywords: Interfacial bonding strength, Metal matrix composites, Tensile strength, Silicon carbide particles | |
5. | Jarecki L., Misztal-Faraj B., Non-linear stress-orientation behavior of flexible chain polymers under fast elongational flow, EUROPEAN POLYMER JOURNAL, ISSN: 0014-3057, DOI: 10.1016/j.eurpolymj.2017.08.028, Vol.95, pp.368-381, 2017Jarecki L., Misztal-Faraj B., Non-linear stress-orientation behavior of flexible chain polymers under fast elongational flow, EUROPEAN POLYMER JOURNAL, ISSN: 0014-3057, DOI: 10.1016/j.eurpolymj.2017.08.028, Vol.95, pp.368-381, 2017Abstract: Closed-form analytical formulas are proposed for non-linear stress-orientation relation valid in the entire range of tensile stresses, intermediate and high, basing on the inverse Langevin chain statistics. Tensile force and orientation characteristics for single, flexible chain macromolecule are reconsidered in a closed-form Padè approximation of the inverse Langevin function in the entire range of chain extensions, as well as the dynamics of molecular deformation and orientation for systems of chains subjected to uniaxial elongational flow. Average stress and orientation tensors, not collinear in the non-linear range, as well as the tensile stress and axial orientation factor of the chain segments in the system are calculated. For the intermediate tensile stresses, the closed-form formula is derived in the first non-Gaussian term approximation of the inverse Langevin function with the assumption of dominating longitudinal elongation of the chains. The high-stress non-linearity formula is derived with the Padè and Peterlin modulus approximations and aligned chain end-to-end vectors by the flow. Both formulas are validated by exact numerical calculations without the assumptions and influence of the approximations is estimated. Ranges of applicability of the formulas are illustrated and examples of their application are presented. Keywords: Molecular orientation, Tensile stress, Non-linear stress-orientation behavior, Elongational flow, Langevin chain statistics | |
6. | Kiełczyński P., Ptasznik S., Szalewski M., Balcerzak A., Wieja K., Rostocki A.J., Thermophysical properties of rapeseed oil methyl esters (RME) at high pressures and various temperatures evaluated by ultrasonic methods, Biomass and Bioenergy, ISSN: 0961-9534, DOI: 10.1016/j.biombioe.2017.09.015, Vol.107, pp.113-121, 2017Kiełczyński P., Ptasznik S., Szalewski M., Balcerzak A., Wieja K., Rostocki A.J., Thermophysical properties of rapeseed oil methyl esters (RME) at high pressures and various temperatures evaluated by ultrasonic methods, Biomass and Bioenergy, ISSN: 0961-9534, DOI: 10.1016/j.biombioe.2017.09.015, Vol.107, pp.113-121, 2017Abstract: Investigation of the high-pressure thermophysical properties of biofuels, e.g., bulk modulus, Surface tension, and viscosity is of paramount importance in fuel injection systems in diesel engines. Another crucial and dangerous phenomenon that may occur in biofuels at high pressures is phase transition (solidification), which can drastically increase the viscosity of the biofuel. This effect may hamper proper operation of the engine, especially under cold-start conditions. Unfortunately, the availability of highpressure thermophysical properties of biofuels is still limited. The goal of this paper is to investigate the impact of high pressures on thermophysical properties of biofuels on the example of rapeseed fatty acid methyl esters (RME) in a wide range of pressures (0:1 to 250 MPa) and temperatures (5 to 20 _C). To this end we employed innovative ultrasonic techniques, i.e., the Bleustein-Gulyaev surface acoustic waves for measuring RME viscosity, and ultrasonic bulk compressional waves for measuring sound velocity in RME and consequently evaluating RME thermophysical parameters, e.g., bulk modulus and surface tension. The viscosity of the measured RME displayed an abrupt increase at pressures: 260 MPa (t Ľ 20 _C), 230 MPa (t Ľ 15 _C), 190 MPa (t Ľ 10 _C), and 130 MPa (t Ľ 5 _C). Evidently it was a signature of the phase transition (solidification) occurring in the RME. The discovered high viscosity high-pressure phase in RME can be very detrimental for operation of modern common rail Diesel engines. Therefore, the results of research presented in this paper should be interesting for engineers and designers working with modern common rail Diesel engines using biofuels. Keywords: Biofuels; Methyl esters; Phase transitions; Viscosity; Speed of sound; Ultrasonic methods; High pressure | |
7. | Banach Z., Larecki W., Kershaw-type transport equations for fermionic radiation, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 0044-2275, DOI: 10.1007/s00033-017-0847-z, Vol.68, No.4, pp.100-1-100-24, 2017Banach Z., Larecki W., Kershaw-type transport equations for fermionic radiation, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 0044-2275, DOI: 10.1007/s00033-017-0847-z, Vol.68, No.4, pp.100-1-100-24, 2017Abstract: Besides the maximum entropy closure procedure, other procedures can be used to close the systems of spectral moment equations. In the case of classical and bosonic radiation, the closed-form analytic Kershaw-type and B-distribution closure procedures have been used. It is shown that the Kershaw-type closure procedure can also be applied to the spectra moment equations of fermionic radiation. First, a description of the Kershaw-type closure for the system consisting of an arbitrary number of one-dimensional moment equations is presented. Next, the Kershaw-type two-field and three-field transport equations for fermionic radiation are analyzed. In the first case, the independent variables are the energy density and the heat flux. The second case includes additionally the flux of the heat flux as an independent variable. The generalization of the former two-field case to three space dimensions is also presented. The fermionic Kershaw-type closures differ from those previously derived for classical and bosonic radiation. It is proved that the obtained one-dimensional systems of transport equations are strictly hyperbolic and causal. The fermionic Kershaw-type closure functions behave qualitatively in the same way as the fermionic maximum entropy closure functions, but attain different numerical values. Keywords: Fermionic radiation, Moment equations, Moment realizability problem, Kershaw-type closure, Three-moment transport | |
8. | Zajączkowska U., Kucharski S., Nowak Z., Grabowska K., Morphometric and mechanical characteristics of Equisetum hyemale stem enhance its vibration, PLANTA, ISSN: 0032-0935, DOI: 10.1007/s00425-017-2648-1, Vol.245, No.4, pp.835-848, 2017Zajączkowska U., Kucharski S., Nowak Z., Grabowska K., Morphometric and mechanical characteristics of Equisetum hyemale stem enhance its vibration, PLANTA, ISSN: 0032-0935, DOI: 10.1007/s00425-017-2648-1, Vol.245, No.4, pp.835-848, 2017Abstract: The order of the internodes, and their geometry and mechanical characteristics influence the capability of theEquisetumstem to vibrate, potentially stimulating spore liberation at the optimum stress setting along the stem.
Equisetum hyemale L. plants represent a special example of cellular solid construction with mechanical stability achieved by a high second moment of area and relatively high resistance against local buckling. We proposed the hypothesis that the order of E. hyemale L. stem internodes, their geometry and mechanical characteristics influence the capability of the stem to vibrate, stimulating spore liberation at the minimum stress setting value along the stem. An analysis of apex vibration was done based on videos presenting the behavior of an Equisetum clump filmed in a wind tunnel and also as a result of excitation by bending the stem by 20°. We compared these data with the vibrations of stems of the same size but deprived of the three topmost internodes. Also, we created a finite element model (FEM), upon which we have based the ‘natural’ stem vibration as a copy of the real object, ‘random’ with reshuffled internodes and ‘uniform’, created as one tube with the characters averaged from all internodes. The natural internode arrangement influences the frequency and amplitude of the apex vibration, maintaining an equal stress distribution in the stem, which may influence the capability for efficient spore spreading. Keywords: Mechanical properties, Plant biomechanics, Segmented structure, Stem vibration, Stress distribution, Wind | |
9. | Jarząbek D.M., Gwiazda M., Dera W., The Influence of Alkali Metal Chloride Treatments on the Wear Resistance of Silicon Surfaces for Possible Use in MEMS, TRIBOLOGY TRANSACTIONS, ISSN: 1040-2004, DOI: 10.1080/10402004.2017.1296211, pp.1-7, 2017Jarząbek D.M., Gwiazda M., Dera W., The Influence of Alkali Metal Chloride Treatments on the Wear Resistance of Silicon Surfaces for Possible Use in MEMS, TRIBOLOGY TRANSACTIONS, ISSN: 1040-2004, DOI: 10.1080/10402004.2017.1296211, pp.1-7, 2017Abstract: The wear of contacting silicon surfaces in microelectromechanical systems (MEMS) has been a longstanding concern. To address this issue, the effects of immersing silicon surfaces into alkali metal chloride solutions (LiCl, NaCl, CsCl) on their sliding friction and wear were investigated. A custom-built reciprocating tribometer was used with a sapphire ball as the counterbody. Results indicated that the friction coefficient between the silicon surface (p-doped, orientation (100)) and a sapphire ball can be reduced by up to 30% by treating the silicon surfaces in aqueous salt solutions (concentration 1 mol/L, exposure for 24 h). These modified surfaces also have higher wear resistance and a significant change in wettability. After immersion, the contact angle between the silicon surface and water was reduced by approximately 50%. These results may lead to new, simple, and inexpensive methods to increase the wear resistance of silicon surfaces for use in MEMs devices. Keywords: silicon surface, wear, friction, alkali metal chlorides | |
10. | Pęcherski R.B., Nowak M., Nowak Z., VIRTUAL METALLIC FOAMS. APPLICATION FOR DYNAMIC CRUSHING ANALYSIS, INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, ISSN: 1543-1649, Vol.15, No.5, pp.431-442, 2017Pęcherski R.B., Nowak M., Nowak Z., VIRTUAL METALLIC FOAMS. APPLICATION FOR DYNAMIC CRUSHING ANALYSIS, INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, ISSN: 1543-1649, Vol.15, No.5, pp.431-442, 2017Abstract: The subject of the study are the models based on digital microstructures, in particular open-cell metallic foams characterized with the skeleton formed of convex or re-entrant cells. Recently, the auxetic materials revealing negative Poisson’s ratio have attracted increasing attention in the context of modern materials applications. Up to date, the research of auxetics is mainly concentrating on the cell structure design and the analysis of quasi-static response. The dynamic properties of such materials are less known. Impact compressions of the two kind of foams under high-velocity are numerically analyzed. To simulate the deformation processes the finite element program ABAQUS is used. The computer tomography makes the basis for the formulation of computational model of virtual foam and the finite element discretization of the skeleton. For numerical simulations the constitutive elasto-viscoplasticity model is applied that defines the dynamic behavior of oxygen-free high conductivity (OFHC) Cu using the experimental data reported in the literature. The numerical predictions of crushing force for velocity 50 and 300 m/s are discussed Keywords: compression test, open-cell copper, convex cell, re-entrant cell, virtual cellular materials, metallic foams, numerical simulation | |
11. | Balcerzak A., Comparison of High-Pressure Behavior of Physicochemical Properties of the Di- and Triacylglycerols Established by Ultrasonic Methods, JOURNAL OF THE AMERICAN OIL CHEMISTS SOCIETY, ISSN: 0003-021X, DOI: 10.1007/s11746-017-3030-y, Vol.94, No.10, pp.1261-1268, 2017Balcerzak A., Comparison of High-Pressure Behavior of Physicochemical Properties of the Di- and Triacylglycerols Established by Ultrasonic Methods, JOURNAL OF THE AMERICAN OIL CHEMISTS SOCIETY, ISSN: 0003-021X, DOI: 10.1007/s11746-017-3030-y, Vol.94, No.10, pp.1261-1268, 2017Abstract: Two samples of triacylglycerols i.e., olive oil and triolein, and one sample of diacylglycerol were investigated.
In the course of compression, the density of the samples was determined by measurements of the change of piston position in a pressure chamber and volume correction due to chamber expansion under pressure. The speed of sound was evaluated from the time of flight of an ultrasonic impulse between emitting and receiving transducers placed in the high pressure chamber. The adiabatic compressibility, the intermolecular free length, the molar volume, the van der Waals’ constant b and the surface tension were evaluated from the density, the speed of sound and the average molecular mass. All tested liquids undergo a high-pressure phase transition. Discontinuities in the measured isotherms of the physicochemical parameters of the investigated oils indicate the presence of high-pressure phase transitions. Moreover the time dependent change of pressure at constant volume during the phase transition was measured. The fundamental difference in the molecular structure of these acylglycerols influences their behavior significantly under high pressure.
Keywords: Acylglycerols; Physicochemical parameters; Ultrasonic measurements | |
12. | Ignaczak J., Domański W., An asymptotic approach to one-dimensional model of nonlinear thermoelasticity at low temperatures and small strains, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2016.1276872, pp.1-10, 2017Ignaczak J., Domański W., An asymptotic approach to one-dimensional model of nonlinear thermoelasticity at low temperatures and small strains, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2016.1276872, pp.1-10, 2017Abstract: A one-dimensional nonlinear homogeneous isotropic thermoelastic model with an elastic heat flow at low temperatures and small strains is analyzed using the method of weakly nonlinear asymptotics. For such a model, both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an elastic heat flow that satisfies an evolution equation. The governing equations are reduced to a matrix partial differential equations, and the associated Cauchy problem with a weakly perturbed initial condition is solved. The solution is given in the form of a power series with respect to a small parameter, the coeﬃcients of which are functions of a slow variable that satisfy a system of nonlinear second-order ordinary differential transport equations. A family of closed-form solutions to the transport equations is obtained. For a particular Cauchy problem in which the initial data are generated by a closed-form solution to the transport equations, the asymptotic solution in the form of a sum of four traveling thermoelastic waves admitting blow-up amplitudes is presented. Keywords: Low temperatures, nonlinear thermoelasticity, small strains, weakly nonlinear asymptotics | |
13. | Sławianowski J.J., Kovalchuk V., Gołubowska B., Martens A., Rożko E.E., Quantized mechanics of affinely-rigid bodies, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, ISSN: 0170-4214, DOI: 10.1002/mma.4501, Vol.40, No.18, pp.6900-6918, 2017Sławianowski J.J., Kovalchuk V., Gołubowska B., Martens A., Rożko E.E., Quantized mechanics of affinely-rigid bodies, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, ISSN: 0170-4214, DOI: 10.1002/mma.4501, Vol.40, No.18, pp.6900-6918, 2017Abstract: In this paper, we develop the main ideas of the quantized version of affinely rigid (homogeneously deformable) motion. We base our consideration on the usual Schrödinger formulation of quantum mechanics in the configurationmanifold, which is given, in our case, by the affine group or equivalently by the semi-direct product of the linear group GL(n,R) and the space of translations R^n, where n equals the dimension of the “physical space.” In particular, we discuss the problem of dynamical invariance of the kinetic energy under the action of the whole affine group, not only under the isometry subgroup. Technically, the treatment is based on the 2-polar decomposition of the matrix of the internal configuration and on the Peter-Weyl theory of generalized Fourier series on Lie groups. One can hope that our results may be applied in quantum problems of elastic media and microstructured continua. Keywords: Homogeneously deformable body, Peter-Weyl analysis, Schrödinger quantization. | |
14. | Roszkiewicz A., Nasalski W., Transmission and reflection properties of two-dimensional finite metal crystals, EUROPEAN PHYSICAL JOURNAL D, ISSN: 1434-6060, DOI: 10.1140/epjd/e2017-70706-9, Vol.71, No.182, pp.1-12, 2017Roszkiewicz A., Nasalski W., Transmission and reflection properties of two-dimensional finite metal crystals, EUROPEAN PHYSICAL JOURNAL D, ISSN: 1434-6060, DOI: 10.1140/epjd/e2017-70706-9, Vol.71, No.182, pp.1-12, 2017Abstract: Optical characteristics of a finite two-dimensional silver stripe photonic crystal of a square lattice are numerically analysed with use of multilayer Rigorous Coupled Wave Analysis. Qualitative changes in optical response of the crystal originated from modifications of the thickness and filling factors of each layer and the polarization direction of the incident wave are shown. The crystal manifests its various characteristics in wideband or narrowband reflection and transmission, while absorption remains low. The behaviour of the crystal is determined by its structure geometry yielding excitation of localized plasmons and collective modes together with interactions between them. The optical response of the square lattice structure is also compared with the response of a triangular lattice crystal. | |