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Molski M.,ckiewicz University Of Poznan

The growth of biological systems described by the Gompertz and West-Brown-Enquist functions is considered in the framework of the space-like supersymmetric quantum mechanics. It has been shown that the supersymmetric effect of a fermion-boson conversion has a biological analogue in the phenomenon of a growth-regression transformation under the influence of a cycle-non-specific drug of a constant concentration. The results obtained reveal that the biological growth can be viewed as the macroscopic quantum phenomenon endowed with the space-like supersymmetric properties not established so far in the domain of biology and medicine. © 2010 Elsevier Ireland Ltd. All rights reserved. Source

Klos J.,ckiewicz University Of Poznan | Lamperski S.,ckiewicz University Of Poznan
Journal of Chemical Physics

Results of the Monte Carlo simulation of the electrode | molten salt or ionic liquid interface are reported. The system investigated is approximated by the primitive model of electrolyte being in contact with a charged hard wall. Ions differ in charges, namely anions are divalent and cations are monovalent but they are of the same diameter d = 400 pm. The temperature analysis of heat capacity at a constant volume Cv and the anion radial distribution function, g2-/2-, allowed the choice of temperature of the study, which is T = 2800 K and corresponds to TO = 0.34 (definition of reduced temperature TO in text). The differential capacitance curve of the interface with the molten salt or ionic liquid at c = 5.79 M has a distorted bell shape. It is shown that with increasing electrolyte concentration from c = 0.4 to 5 M the differential capacitance curves undergo transition from U shape to bell shape. © 2014 AIP Publishing LLC. Source

Gorniak R.,ckiewicz University Of Poznan | Lamperski S.,ckiewicz University Of Poznan
Electrochimica Acta

Grand canonical Monte Carlo simulation results are reported for an electric double layer composed of a graphene electrode and spherical ions. The electrode is a honeycomb structured corpuscular carbon with a partial point electric charge immersed at the centre of each carbon atom. Ions are approximated by soft spheres with a point electric charge located at the centre. The soft ion-ion and carbon-ion interactions are describe by the Lennard-Jones (LJ) potential. The diameter of anions is fixed as r0,- = 300 pm (r0 is the LJ potential parameter) while that of cations, r0,+, takes the following values: 250, 300, and 350 pm. The ion charge numbers are +1 and -1, respectively, for cations and anions. Results for the graphene electrode-ion singlet distributions, the mean electrostatic potential and differential capacitance are obtained for the electrolyte concentrations c = 1, 2 and 3 mol/dm3 and the electrode charge density varying from -0.9 to +0.9 C/m2 at the relative permittivity 78.5 and temperature 298.15 K. It is found that at the negative electrode charges, with increasing cation diameter the cation singlet distribution maximum is shifted towards greater distances from the electrode and the height of the maximum is elevated. For high negative and positive values of the electrode charges another layer of cations is observed to appear. With increasing an electrolyte concentration the shape of differential capacitance curve changes from that with a minimum surrounded by maxima, through a plateau preceded by a single maximum into that of a distorted bell. © 2016 Elsevier Ltd. All rights reserved. Source

Gorniak R.,ckiewicz University Of Poznan | Lamperski S.,ckiewicz University Of Poznan
Journal of Physical Chemistry C

Structural and thermodynamic properties of the electric double layer with a graphene electrode are investigated by the grand canonical Monte Carlo simulations. The nonelectrostatic carbon-ion and ion-ion interactions are described by the Lennard-Jones potential. The results (the ion singlet distribution functions, the mean electrostatic potential, the integral, and the differential capacitance) for an explicit corpuscular structure are compared with those obtained for the structureless carbon sheet and hard surface electrodes. Simulations are carried out for 1.0 mol/dm3 1:1 electrolyte at T = 298.15 K and εr = 78.5 in the range of the electrode surface charge density from -0.9 to +0.9 C/m2. The surface density of carbon atoms in graphene is 5.03066 × 1019 m -2. The singlet distribution functions of ions show that the ion adsorption at the carbon electrodes is evidently stronger than that at the hard surface electrode. The profiles of the mean electrostatic potential near the positively charged carbon electrodes have a minimum that is characteristic of divalent anions near a hard surface electrode. For both carbon electrodes, the integral and differential capacitance curves have the bell shape with a broad maximum, while the curve for the hard surface electrode has a camel-like shape with two humps. The difference between the graphene and structureless carbon electrodes is manifested mainly in capacitance. In the range of a small magnitude of electrode charges, the capacitance results for the graphene electrode are smaller than those for the structureless carbon electrode. © 2014 American Chemical Society. Source

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