Wyniki wyszukiwania - BazTech

1

Computer-based simulation of plasma concentration time-proﬁles of drug in nonlinear two-compartment model

Piekarski S., Kiełczyński P., Szalewski M., Rewekant M.

Computer Assisted Methods in Engineering and Science

|

2013

|

Vol. 20, no. 4

279--288

EN

The main interest of pharmacokinetics is the study of the fate of drugs in the living organism. This work proposes the system of the conservation laws that describes time-dependent concentrations of a drug, after a single intravenous administration. Compared with others, the proposed model considers both free and protein-bound drug concentrations at the same time. Plasma protein binding captured in the model enters the nonlinearity arising from the Guldberg-Waage law. According to our best knowledge, the analytical solution for our system does not exist. Our model allows the calculation of the free and bound-drug protein concentrations at any time point and at any dose after single intravenous bolus dose administration. In order to compare the empirical with simulated data, a numerical approach has been proposed. On the basis of published experimental data the model validation has been carried out. The goodness of ﬁt was satisfactory (R 2 = 0.99) and the experimental and simulated AUC (area under the curve) values, as the measure of the bioavailability of drug, were similar (150 M/hxh−1). The preliminary assessment of the model credibility was positive and encouraged further studies.

2

Systemy zarządzania logistycznego w przedsiębiorstwie prowadzącym autoryzowaną dystrybucję pojazdów i maszyn rolniczych

Juściński S., Piekarski S.

Zarządzanie Przedsiębiorstwem

|

2009

|

Vol. 12, nr 2

42-48

EN

The article presents basic objectives and tasks carried out within logistic management of a trade-service enterprise. The object of the research is a company running authorised distribution of agricultural tractors and machines, spare parts and services of products. The processes in the trade and service company providing services for the sector of food producers can be divided into: logistics of the trade department, logistics of the sales department of spare parts and operation fluids, as well as logistics of the maintenance service station. All the above mentioned subsystems complement each other on particular stages of the logistic chain, ensuring the optimal customer service. The sales procedure of new agricultural tractors by the Commercial Department has been presented. The distribution of tractors can be performed according to four routes of fulfilment of orders placed by the consumer. The shortest procedure is applied when the required model is available at the dealer's location. The tractor can also be ordered from the National Logistic Centre or from other company's supplies, if the company constitutes an element of the distribution network. The longest route pertains to the situation when the order is placed via email directly to the factory producing a given model. The system of spare parts sale within a logiparts is satisfied with the use of logistic solutions, which enhance the speed and reliability of commodity flow in the supply chain. The structure of distribution of spare parts for farm tractors and machines functions as a net with the following elements: the European Logistic Centre, the National Logistic Centre and regional wholesale stores run by dealer companies. Kinds of orders made by a commercial company in the National Logistic Centre of the manufacturer and a procedure compulsory for ordering spare parts for individual needs of a customer have been characterised. Supplying the stocks is generated in the IT system after reaching the safety level by spare parts and it takes a form of timely orders or special order. Preparing the document of an individual order is preceded by the process of verification of the required parts in order to establish their catalogue code, taking into consideration construction changes for a given type and year of a given tractor or a farm machine. The participation of employees in the process of technical completion is aimed at eliminating errors and mistakes at the preliminary stage of the order. The occurrence of inconsistencies in each case lowers the level of customer service and is a reason of losses for the company and the purchaser. Accepting the order results in its immediate transfer to the National Logistic Centre via email. Logistic tasks in the procedure of performing warranty and post-warranty services by the Service Department as well as the procedure of spare parts supply, necessary for the fulfilment of accepted orders, have been presented. When establishing a current schedule, the Service Department takes the following factors into consideration: the availability of spare parts, the time of repair and the market demand for maintenance services in a given period of the year. The structure of logistic system of spare parts distribution is based on three levels of availability. The location in the wholesale store of the dealer makes it possible to receive the parts immediately; ordering them at the National Logistic Centre involves waiting for 24 hours, while supplies from the European Logistic Centre are carried out within 48 hours. The logistic management is a kind of activity based on fulfilling precisely established goals. A perfect organisation and professional technical service, with a simultaneous care for high effectiveness, require concentrating efforts and means on ensuring the flow of products for sale at the level which satisfies the market demand.

3

Galilean-invariant formulation of the fluid mechanics

Piekarski S.

Prace Instytutu Podstawowych Problemów Techniki PAN

|

2007

|

nr 7

1-103

EN

It seems that an approach, discussed in this text, started in 1991; then the notions of the "amorphous Galilean space-time" and the "Galilean space-time with measurable time intervals" have been introduced in S?lawianowski's monograph [1] and the notion of the "non-relativistic four-velocity" has been introduced in [2] by Piekarski. In the present text applications of the non-relativistic four-velocity in fluid mechanics and kinetic theory are discussed. The most direct application of the non-relativistic four-velocity is that it allows one to construct inertial coordinate systems explicitly, that is, in terms of the four-dimensional affine geometry (see [3]). The Galilean space-time and the Minkowski space-time are both four-dimensional affine spaces and an important difference is that the first one possess a "canonical" family of parallel hyperplanes of simultaneous events. In order to analyse Galilean-invariant field equations (like Navier-Stokes-Fourier theory) one has to understand the nature of differential operators on the "amorphous Galilean space-time" and related spaces [1]. In 1992, the differential operators on the amorphous Galilean space-time have been introduced using the "dual" approach of Peradzy´nski by Piekarski (compare [4, 5, 6], see also [7, 8, 9, 10]). Alternatively, one can use the definition of the complete derivative in the normed affine space given in Schwartz's monograph [11]. This definition can be applied in finite-dimensional affine spaces since all norms in the corresponding translation spaces are equivalent. In Galilean spacetime (which is a four-dimensional affine space) the hyperplanes of simultaneous events are the three-dimensional affine spaces what implies a coexistence of two "canonical" complete derivatives; one is the "four-dimensional" and the second one is the "three-dimensional" (some results on that subject are given in [3], together with the observation that the "substantial derivative" of the fluid mechanics is a directional derivative along the non-relativistic four-velocity). In the present text it is shown that the Navier-Stokes-Fourier equations can be written invariantly. The invariant interpretation of the Gibbs identity is given (see Eqs. (3.43)-(3.53)). vi Preface Some invariant aspects of the non-relativistic kinetic theory are also discussed. The potential application of our approach is the problem of the symmetry group for the fluid mechanics and the kinetic theory. As it is well-known, in continuum mechanics one usually applies the "principle of the material indifference" (see, for example, Jemio?lo and Telega [12]) but at the same time some scientists stress that in the kinetic theory of gases such quantities as the heat flux have non-objective macroscopical constitutive laws ([13], p. 97). It is not excluded that the above mentioned discrepancy could be eliminated after formulating the fluid mechanics and the kinetic theory in the manner invariant with respect to the automorphisms of the Galilean space-time. Our hypotheses on this subject is discussed shortly in the last chapter and in Appendix F (the adequate formalism here is Rychlewski's theory of "?-structures" [45] for "affine" automorphisms of Galilean group acting on the Galilean space-time). Readers uninterested in Galilean invariance can read the second chapter only, where the results of this text concerning the Navier-Stokes-Fourier equations are written in the standard notation. In particular, new solutions of the Gibbs identity for dense fluids are found and the corresponding sound speeds are computed. It is hoped that our approach shall be applied in acoustics of fluids (part of our main results shall be published in Archives of Acoustics, [17]). In medical acoustics, biological tissues are often modelled as the dense fluids [47, 67] what gives strong motivation for developing of mathematical methods in the modelling of dense fluids.

PL

Przedstawiona praca dotyczy sformułowania mechaniki cieczy w jezyku nierelatywistycznej czasoprzestrzeni Galileusza (jako struktury algebraicznej) oraz niezmienniczości operatorów różniczkowych i równań. Treść rozprawy jest kontynuacją wcześniejszych wyników, które otrzymano w roku 1991, gdy to Sławianowski wprowadził modele czasoprzestrzeni Galileusza ("amorphous Galilean spacetime" i "Galilean space-time with measurable time distances") opisane w [1] oraz autor wprowadził w [2] pojęcie "nierelatywistycznej czteropredkości". Niektóre wyniki, opisane w rozprawie, zostały opublikowane przez autora niedawno [16, 17], natomiast na ostateczna treść miały wpływ zarówno wcześniejsze prace autora o niezmienniczych definicjach równań cząstkowych na przestrzeniach afinicznych i przestrzeniach afinicznych z dodatkowymi strukturami [3, 4, 7-10] jak i prace dotyczące niezmienników w ogólnorelatywistycznym rachunku perturbacyjnym, wykonane przez autora wspólnie z Z. Banachem [58-65]. Najwięcej uwagi poswięcono równaniom Naviera-Stokesa-Fouriera i ich konsekwencjom. Z punktu widzenia zastosowań, najważniejsze wydają sie wyniki dotyczące gestych cieczy, które zostały opisane w "standardowej" notacji w rozdziale drugim (zostały one częściowo opublikowane w artykułach [16, 17]). "Tożsamości termostatyczne" otrzymuje się tam jako konsekwencje równań Naviera-Stokesa- Fouriera a jako pola pierwotne przyjmuje gęstość masy i temperature T. Opisano tam propozycje autora, aby "gęstą ciecz" definiować poprzez warunek, że gęstość energii (na jednostkę masy) zależy nie tylko od temperatury T, ale także od gęstości masy. W przedstawionej rozprawie (i w pracach [16, 17]) autor pokazał, ze jesli gestosc energii na jednostke masy zależy tylko od temperatury oraz jednocześnie spełniona jest tożsamość Gibbsa, to ciśnienie jest dowolną funkcją od gestości masy mnożoną przez temperature T. Podano nowe rozwiazania dla tożsamości Gibbsa, opisujące w szczególności gęste ciecze i obliczono odpowiednie prędkości dźwieku. Pokazano, że w ramach zaproponowanego podejścia można opracowaćprzyblizona klasyfikacje gęstych cieczy, która w szczególności może przypominać rozwinięcia wirialne i, dla przykładu, zbadano proste przypadki "gęstych cieczy". Modele gęstych cieczy mogą być użyteczne np. dla akustyki medycznej, gdzie często tkanki biologiczne są modelowane jako gęste ciecze. Przedstawione w rozprawie wyniki mają tylko zilustrować proponowane podejście i uzasadnić celowość kontynuowania badań. Przy badaniu gęstych cieczy, Galileuszowskie niezmienniki pomogły uścislić dyskusje. Jednoczesnie, Galileuszowska niezmienniczość operatorów rózniczkowych i równań pola może bycćosobnym tematem badań i niezmiennicze zapisanie równan Naviera-Stokesa-Fouriera zostało ułatwione dzięki obserwacji autora, ze "pochodna substancjalna" nierelatywistycznej hydrodynamki kontinuum jest pochodną kierunkową w kierunku "nierelatywistycznej czteroprędkości" [3]. W przedstawionej rozprawie dyskutowane są też niektóre fakty, dotyczące niezmienniczych aspektów nierelatywistycznej teorii kinetycznej. W rozdziale czwartym podano niezmiennicze sformułowanie nierelatywistycznej funkcji rozkładu (z włączeniem rozkładów kwantowych w przybliżeniu bezspinowym). W rozdziale piatym dyskutowane jest równanie Boltzmanna. Jednym z aspektów teorii kinetycznej sa równania momentowe; ogólna postac równan momentowych dla równania Boltzmanna została opublikowana przez autora (wspólnie z Z. Banachem) w roku 1989 [56]. Jednak podane tam równania nie są zapisane poprzez niezmienniki i sposób, w jaki pojawiają się "niezmiennicze" momenty w nierelatywistycznej teorii kinetycznej jest krótko omawiany w rozdziale piątym. Aby lepiej zrozumieć operatory rózniczkowe stosowane przy niezmienniczym zapisie równań Naviera-Stokesa-Fouriera, w dodatkach opisujemy kanoniczne operatory rózniczkowe na rozwazanych "modelach" czasoprzestrzeni Galileusza. W dodatkach szczególną uwagę zwracamy też na te podgrupy automorfizmów rozwazanych przestrzeni, dla których zbiorami punktów stałych sa proste afiniczne. Mamy nadzieję, że badanie takich przekształceń dla czasoprzestrzeni Galileusza mogłoby pomóc przy dyskusji "zasady obiektywności materialnej". Warto podkreslic, że zarówno przy wprowadzaniu "nierelatywistycznych" niezmieników (opisywanych w przedstawionej pracy) jak i przy wprowadzaniu niezmienników dla ogólnorelatywistycznego rachunku perturbacyjnego (wprowadzonych wspólnie z Z. Banachem, [58-65]) nie korzystano z teorii reprezentacji grup. Skonczeniewymiarowe przestrzenie afiniczne "z dodatkowymi strukturami" opisujemy jako odpowiednie "struktury algebraiczne" i opisujemy niektóre ich automorfizmy. Tak otrzymywane grupy automorfizmów są jednocześnie grupami Lie przekształceń, ale ten aspekt, podobnie jak "teoriomnogościowe" sformułowanie teorii grup przekształceń Rychlewskiego [45], jest poza zakresem przedstawionej pracy.

4

On the classification of dense fluids

Piekarski S.

Archives of Acoustics

|

2007

|

Vol. 32, No. 4

933--940

EN

It is commonly accepted that the existence of entropy imposes restrictions on the constutive functions in the Navier-Stokes-Fourier equations. In the paper: S. Piekarski, "On the Navier- Stokes equation for water" (Archives of Acoustics, 31, 2, 265271, 2006) it has been shown that if the energy per unit mass is a function of the temperature T only, then the pressure p is an arbitrary function of the density - multiplied by the temperature T. Now the general form of the relations between the energy density and the pressure is given (both quantities are understood as functions of the mass density and the temperature). These relations can be approximated in different ways and different approximations suggest different classifications of dense fluids (some of them are similar to the virial expansions).

5

On the Navier-Stokes equations for water

Piekarski S.

Archives of Acoustics

|

2006

|

Vol. 31, No. 2

265-271

EN

In general, the existence of entropy imposes restrictions on the constitutive functions in the Navier-Stokes equations. In this paper, it is shown that if the energy per unit mass is a function of the temperature Τ only, then the pressure p is an arbitrary function of the density ρ multiplied by the temperature Τ. However, for many fluids with the properties radically different than ideal gases (the best example here is water) the pressure as a function of ρ and Τ is not of the form p0(ρ)Τ. Therefore the energy density per unit mass in the Navier-Stokes equations for water should depend also on the mass density and the explicit form of this dependence requires further discussion.

6

Stress-assisted diffusion and the modified Fick law

Piekarski S.

Journal of Technical Physics

|

2005

|

Vol. 46, no 1

3-7

EN

It can be observed that the equation for "stress-assisted diffusion" applied by Shewmon (P.G. Shewmon, Diffusion in solids, McGraw-Hill, 1963) is simply the Einstein-Smoluchowski equation. In turn, for a constant temperature field, the modified Fick law (introduced in: S. Piekarski, On the modified Fick law and its potential applications, J. Tech. Phys., 44, 2, 125-131, 2003) reduces to the Einstein-Smoluchowski equation. Therefore, the solutions of the modified Fick law can be adopted to the problems considered by Shewmon. In this paper, the problems of diffusion and thermodiffusion in the strain fields of dislocations (screw and edge) are considered and new solutions are briefly discussed.

7

On the thermodiffusion equation for electrically charged matter

Piekarski S.

Journal of Technical Physics

|

2005

|

Vol. 46, no 2

83-95

EN

In this paper, we propose the thermodiffusion equation for electrically charged matter. It is a generalisation of the modified Fick law, which has been introduced in the paper: S. Piekarski, "On the modified Fick law and its potential applications" (J. Tech. Phys., 44, 2, 125-131, 2003). In the modified Fick law there exists a potential force acting on the diffusing matter which is described as the gradient of the potential U(x). Now we replace U(x) by U(x) - q[phi](x,t) where [phi] is the electrostatic potential, while q is the electric charge of a diffusing carrier. We write the corresponding field equations and consider the electromotive force induced by the temperature gradient. It is easy to compute this force under the assumption that the system is quasineutral. However, it seems that a more realistic model of the electromotive force induced by the temperature gradient should allow a deviation from quasineutrality. Both versions are compared and it is interesting whether the resulting expressions can be verified experimentally.

8

On the modified Fick law and its potential applications

Piekarski S.

Journal of Technical Physics

|

2003

|

Vol. 44, no 2

125-131

EN

It can be observed that the standard Einstein-Smoluchowski equation for isothermal processes can be written in the two equivalent forms which, however, become distinct when the temperature becomes spatially varying. Therefore, we have two different equations which could potentially describe the flux of diffusing particles subjected to the potential external forces and variable temperature. The first is the standard Einstein-Smoluchowski equation, while the second is its modification containing an additional term proportional to the temperature gradient. In order to fix the terminology, the above mentioned modification of standard Einstein-Smoluchowski equation shall be called '^the modified Fick law". In this paper, we shall discuss the origin of this equation and we shall try to make a preliminary discussion of its solutions and potential applications to thermodiffusion. We propose two models: one exploiting Onsager's thermodynamics and the second one independent from it. Elementary solutions of both models are identical in the limit of small concentrations.

9

On diffusion and thermodiffusion in a gravity field

Piekarski S.

Journal of Technical Physics

|

2003

|

Vol. 44, no 3

329-337

EN

The modified Fick law has been introduced in the paper: S. Piekarski, On the modified Fick law and its potential applications (J. Tech. Phys., 44, 2, 125-131, 2003). The first purpose of the present paper is to give a simpler "derivation" of the modified Fick law than that originally presented. Namely, it can be introduced as a particular case of the Wojnar equation (R. Wojnar, "Nonlinear heat equation and thermodiffusion", p. 296, Eq. (2.1), Rep. on Math. Phys., No 1/2, Vol. 46, 2000). The third equation discussed is the Einstein-Smoluchowski equation. All equations mentioned above, contain a potential for the force, acting on the diffusing matter. The important fact is that, for isothermal conditions, all the equations mentioned above are identical. In this article we try to describe the effects of the constant gravitational field on the diffusion processes. We propose an explicit form of the potential for which the equilibrium concentration profiles are consistent with the experimental results. We compare shortly our results with two models of the diffusion processes in a gravitational field described in Huang's book [8] as well as with other opinions concerning this subject. As an example of technological application of the presented theory, the diffusion of the atomic hydrogen in fluid iron is proposed.