Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls

We analyze the lateral critical Casimir force acting between two planar, chemically inhomogeneous walls confining an infinite 2D Ising strip of width $M$. The inhomogeneity of each of the walls has size $N_1$; they are shifted by the distance $L$ along the strip. Using the exact diagonalization of the transfer matrix, we calculate the lateral critical Casimir force and discuss its properties, in particular its scaling close to the 2D bulk critical point, as a function of temperature, surface magnetic field, and the geometric parameters $M$, $N_1$, $L$. We determine the magnetization profiles which display the formation of the bridge joining the inhomogeneities on the walls and establish the relation between the characteristic properties of the lateral Casimir force and magnetization morphologies. We check numerically that breaking of the bridge is related to the inflection point of the lateral force.Comment: 5 pages, 6 figure

Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results

We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to $+h_1$ except for a group of $N_1$ sites where it is equal to $-h_1$. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance $L$. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for a wide range of temperatures and system parameters. The lateral critical Casimir force tends to reduce the shift between the inhomogeneities, and the excess normal force is attractive. Upon increasing the shift $L$ we observe, depending on the temperature, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on $L$. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for a whole range of different models of the strip with the same type of inhomogeneity

Design of GPS-GPRS module for localization vehicles and cargo

In the paper are presented results of market researches of logisticenterprises in Upper Silesia region which determine the level of implementation of GPS systems in vehicles. The results of that research implied design of GPS-GPRS module to be applied in vehicles as an alternative solution for modules already present on the market

Critical Casimir forces between defects in the 2D Ising model

An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here

New developments for ALICE MasterClasses and the new Particle Therapy MasterClass

International MasterClasses (IMC), an outreach activity of the International Particle Physics Outreach Group (IPPOG), has been bringing cutting-edge particle physics research to schoolchildren for over 15 years now. All four LHC experiments participate in the event, including ALICE, the experiment optimised for the study of heavy-ion collisions. Heavy-ion physics is actively contributing to IMC with new developments including experimental measurements but also applications for society, such as treatment of cancer with ions. In particular, ALICE provides three MC measurements related to the main observables used to characterize the properties of the produced Quark-Gluon Plasma. Historically, those MC measurements were developed independently, inheriting from the first one, by several ALICE groups. Since all of them are based on the ROOT EVE package, a project to integrate them into a common framework was undertaken. ALICE delivers now a single and easy-to-use application, compiled under Linux, MacOS, and, for the first time, Windows. Then, in line with current IPPOG goals to increase the global reach and scope of the IMC programme a newly developed measurement on medical applications of particle physics, the Particle Therapy MasterClass (PTMC) was introduced in the IMC2020 programme. It is a simplified version of matRad, a MATLAB-based toolkit for calculation of dose deposition in the body and allows for planning of radiotherapy using different modalities and highlighting the benefits of treatment with ions.Comment: 7 pages, 3 figures, proceedings of the 24th International Conference on Computing in High Energy and Nuclear Physics (CHEP 2019

Logistics system of collection, dismantling and recycling of end-of-life vehicles

In the paper it is presented system for collection, dismantling and recycling of end-of-life vehicles. There are discussed framework of the system based on ELV European directive and Polish act. It is presented profitability of recycling of typical vehicles in Poland and methods of effective preparation of wrecks for shredding and further steel production. Examples are presented for Upper Silesia area

Dynamic programming approach to structural optimization problem – numerical algorithm

In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed

Characterization of the algebraic difference of special affine Cantor sets

We investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \mathbb{N}$, $l+r<p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems.Comment: This paper was previously a part of the submission arXiv:2102.11194v

The algebraic difference of central Cantor sets and self-similar Cantor sets

Let $C(a),C(b)\subset [0,1]$ be the central Cantor sets generated by sequences $a,b \in (0,1)^{\mathbb{N}}$. The main result in the first part of the paper gives a necessary condition and a sufficient condition for sequences $a$ and $b$ which inform when $C(a)-C(b)$ is equal to $[-1,1]$ or is a finite union of closed intervals. In the second part we investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \mathbb{N}$, $l+r<p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval

Deontological considerations on academic collaboration in Poland

The author conducted deontological deliberations concerning collaboration among academic workers in the reality of Polish universities. In the view of potential irregularities that threaten this cooperation, it has been investigated what answer is brought in this regard by the ethical codes of universities but also how this problem is perceived by the students who tend to be critical and keen observers. As far as codification is concerned of standards related to the issue in question, Polish academic environment is not in a bad condition. It seems that the problem has been noticed. However, when those documents are perceived as a collection of not so much written, but rather actually recognized values, then the quoted remarks of the students would prove that there is more work to be performed in this respect, which should be deepened under studies of quantitative and qualitative nature. One clear conclusion is drawn from the performed analyses. Namely undermining the authority of one academic by another - in particular in the eyes of the students - results not only in weakening the authority of the humiliated person but mainly of the humiliating individual. Moreover, it contributes to straining the authority of an academic as such