Numerical simulations of anomalous diffusion

In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is a phenomenon connected with the interactions within the complex and non-homogeneous background. In order to consider physical initial-value conditions we use fractional derivative in the Caputo sense. In numerical analysis the boundary conditions of first kind are accounted and in the final part of this paper the result of simulations are presented.Comment: 5 pages, 2 figures, CMM 2003 Conference Gliwice/Wisla Polan

Numerical solution of fractional Sturm-Liouville equation in integral form

In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the integral form. Next the numerical scheme is presented. In the final part of this paper examples of numerical solutions of this equation are shown. The convergence of the proposed method on the basis of numerical results is also discussed.Comment: 14 pages, 3 figures, 2 table

Zdzisław Zmigryder Konopka – ancient militaty historian, classical philologist, historian of roman law and teacher

Zdzisław Zmigryder-Konopka, Warsaw philologist, historian of the antique military, Roman law and teacher, engaged with antiquity in many ways during his scholarly and teaching career. Above all, however, he was trained as a philologist and for a certain period (when not employed at the university) he was even a teacher of Latin and Greek in secondary schools, where he enjoyed recognition among pupils and students. In his research work – interrupted by his untimely passing – he focused on Roman history, but his studies spanned a broad chronological timeframe and diverse range of topics, namely Roman law (social and constitutional) and military history. He was a man utterly fascinated by his field and working with young people, not to mention his public activism. He was the type of true humanist whose values, formed and embraced during university studies, shaped and permanently influenced his attitude to life. In the final period of his life, with the rise of anti-Semitism and growing threat of war, Zdzisław Zmigryder-Konopka became a member of the National Committee for Aid to Jewish Refugees from Germany. In addition, he became involved with the Social Committee for the Defence of the State as part of the Jewish Community in Warsaw. After the outbreak of the war, he volunteered to fight in the September campaign, and after it ended he arrived in Lwów to become a lecturer at the Jan Kazimierz University. Though affected by poor health and chronic illness, his death on 4 November 1939 still came as a surprise. Discussed more broadly in this paper, Zmigryder-Konopka’s “Battle in the Teutoburg Forest” relied on an analysis of source text to deliver a substantive response to the assertions published in German scholarly literature of the 1930s, which eulogized Germanic past in European history following Germany’s defeat in the Great War of 1914-1918 and Adolf Hitler’s rise to power.Zdzisław Zmigryder-Konopka, Warsaw philologist, historian of the antique military, Roman law and teacher, engaged with antiquity in many ways during his scholarly and teaching career. Above all, however, he was trained as a philologist and for a certain period (when not employed at the university) he was even a teacher of Latin and Greek in secondary schools, where he enjoyed recognition among pupils and students. In his research work – interrupted by his untimely passing – he focused on Roman history, but his studies spanned a broad chronological timeframe and diverse range of topics, namely Roman law (social and constitutional) and military history. He was a man utterly fascinated by his field and working with young people, not to mention his public activism. He was the type of true humanist whose values, formed and embraced during university studies, shaped and permanently influenced his attitude to life. In the final period of his life, with the rise of anti-Semitism and growing threat of war, Zdzisław Zmigryder-Konopka became a member of the National Committee for Aid to Jewish Refugees from Germany. In addition, he became involved with the Social Committee for the Defence of the State as part of the Jewish Community in Warsaw. After the outbreak of the war, he volunteered to fight in the September campaign, and after it ended he arrived in Lwów to become a lecturer at the Jan Kazimierz University. Though affected by poor health and chronic illness, his death on 4 November 1939 still came as a surprise. Discussed more broadly in this paper, Zmigryder-Konopka’s “Battle in the Teutoburg Forest” relied on an analysis of source text to deliver a substantive response to the assertions published in German scholarly literature of the 1930s, which eulogized Germanic past in European history following Germany’s defeat in the Great War of 1914-1918 and Adolf Hitler’s rise to power

Numerical simulation of the heating process in the domain of tissue insulated by protective clothing

In this paper the 2D heterogeneous tissue domain (forearm cross-section) insulated by a layer of protective clothing is considered. The aim of considerations is to develop an algorithm simulating the tissue heating process resulting from the sudden change of external boundary conditions. Here, the authors exploit a certain version of the control volume method (CVM) using the Voronoi tessellation. The mathematical model of heat exchange in the domain analyzed is formulated in the form of a boundary-initial problem based on the system of partial differential equations (energy equations) supplemented by the adequate boundary and initial conditions. In the final part of the paper, the examples of numerical simulations are shown

Numerical solution of non-homogenous fractional oscillator equation in integral form

In this paper, a non-homogenous fractional oscillator equation in finite time interval is considered. The fractional equation with derivatives of order α ∈ (0, 1] is transformed into its corresponding integral form. Next, a numerical solution of the integral form of the considered equation is presented. In the final part of this paper, some examples of numerical solutions of the considered equation are shown

Analytical solution of the dual phase lag equation describing the laser heating of thin metal film

Heat transfer processes occurring in the micro-domains can be described using the dual-phase lag equation (DPLE). This equation can be applied as a model of heating of the thin metal film subjected to the femtosecond laser pulse. In the paper, the 1D dual phase lag equation containing the additional internal heat source resulting from the laser pulse irradiation and supplemented by the appropriate boundary and initial conditions is considered. Appearing in this equation two lag times τq the phase lag of the heat flux) and τT (the phase lag of the temperature gradient) are taken into account. An analytical solution of this equation under the assumption that τT > τq is presented. The separation of the variables technique and the Green’s function method are used in order to find this solution. In the final part of the paper, the example of computations is presented

Kształtowanie się Europy

Recenzja książki: Peter Heather, Imperia i barbarzyńcy. Migracje i narodziny Europy, przeł. J. Szczepański, Dom Wydawniczy REBIS, Poznań 2010, 766 s., z mapami, indeksam

Historia Greków

Recenzja książki: Sarah B. Pomeroy, Stanley M. Burstein, Walter Donlan, Jennifer Tolbert Roberts, Starożytna Grecja. Historia polityczna, społeczna i kulturalna, z ang. przeł. O. Dragouni, Książka i Wiedza, Warszawa 201

Roma aeterna.

Recenzja książki: Peter Heather, Odrodzenie Rzymu. Cesarze i papieże: bój o władzę nad chrześcijaństwem, przeł. J. Szczepański, Dom Wydaw¬niczy Rebis, Poznań 2014, 514 s. z ilustracjami i mapamistron