Browsing by Author "Dimitrova I.M."
Now showing 1 - 14 of 14
Results Per Page
Sort Options
Item Callen–Welton fluctuation dissipation theorem and Nyquist theorem as a consequence of detailed balance principle applied to an oscillator(2019-09-15) Mishonov T.M.; Dimitrova I.M.; Varonov A.M.We rederive the Nyquist theorem and Callen–Welton fluctuation dissipation theorem as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the consideration understandable for every physicists. Perhaps it is the simplest derivation of these well-known theorems in statistical physics. The classical limit is understandable as a consequence of Waterston–Herapath equipartition theorem.Item Determination of the Boltzmann constant by the equipartition theorem for capacitors(2019-04-08) Mishonov T.M.; Gourev V.N.; Dimitrova I.M.; Serafimov N.S.; Stefanov A.A.; Petkov E.G.; Varonov A.M.A new experimental set-up for measurement of the Boltzmann constant is described. The statistically averaged square of voltage U2 is measured for different capacitances C. The Boltzmann constant is determined by the equipartition theorem C U2 k T = . For fixed capacitance, voltages could be measured for different temperatures. The set-up consists of low-noise, highfrequency operational amplifiers ADA4898-2. An instrumental amplifier is followed by an inverting amplifier, the square of the voltage is created by an analog multiplier AD633, and finally, the averaged signal is measured by a multimeter. More than ten high-school students were able to measure the Boltzmann constant with the experimental set-up in the 5th Experimental Physics Olympiad with excellent accuracy compared to the price, conditions and available time for the experiment. A new derivation of the important statistical physics theorems by Nyquist and Callen-Welton is given in an appendix at the level of introductory courses in physics studied by future teachers. To understand the work of the experimental set-up, it is only necessary to know the equipartition theorem.Item From the molecular quadrupole moment of oxygen to the macroscopic quadrupolarizability of its liquid phase(2019-08-14) Slavchov R.I.; Dimitrova I.M.; Menon A.Liquid oxygen is an example for a quadrupolar medium - a dense fluid made of nonpolar molecules carrying a significant quadrupolar moment. In this work, we present a method for the computation of the macroscopic quadrupolarizability of such a quadrupolar liquid. As a first step, the quadrupole moment and the molecular quadrupolarizability of O2 are calculated from first principles. Next, we apply a model generalizing Onsager's dielectric cavity theory to compute the macroscopic quadrupolarizability of liquid oxygen under a wide range of conditions. Literature data for the density and dielectric permittivity of oxygen are used to determine the cavity size independently.Item Master equation for operational amplifiers: Stability of negative differential converters, crossover frequency and pass-bandwidth(2019-02-26) Mishonov T.M.; Stefanov A.A.; Petkov E.G.; Dimitrova I.M.; Danchev V.I.; Varonov A.M.The well forgotten master equation from the seminal article by Ragazzini, Randall and Russell [J. R. Ragazzini, R. H. Randall and F. A. Russell, ``Analysis of Problems in Dynamics by Electronic Circuits``, Proc. of the I.R.E., 35, pp. 11-19, (1947)] is recovered as indispensable tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage U 0 (t) and the difference between the input voltages (U + (t) and U - (t)). The crossover frequency f 0 parameterizes the time constant τ 0 of this equation. The work of the master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications. A simple circuit for determination of f 0 is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is indispensable.Item Master equation for operational amplifiers: Stability of negative differential converters, crossover frequency and pass-bandwidth(2019-03-01) Mishonov T.M.; Danchev V.I.; Petkov E.G.; Gourev V.N.; Dimitrova I.M.; Serafimov N.S.; Stefanov A.A.; Varonov A.M.The time dependent master equation from the seminal article by Ragazzini, Randall and Russell (Ragazzini et al 1947 Proc. of the I.R.E. 35, 444–452) is recovered as a necessary tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage U0(t) and the difference between the input voltages (U+(t ) and U-(t )). The crossover frequency f0 is represented with the time constant τ in this equation. The work of the 0 master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications without citations of the time dependent equation. A simple circuit for determination of f0 is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is a useful technique implicitly included in the contemporary software. The frequency dependent formulae for the amplification coefficient of inverting and non-inverting amplifiers are given for the case of non-zero conductivity between the inputs of the operational amplifiers.Item Measuring the Equilibrium Spreading Pressure—A Tale of Three Amphiphiles(2024-09-01) Peychev B.; Arabadzhieva D.; Minkov I.L.; Dimitrova I.M.; Mileva E.; Smoukov S.K.; Slavchov R.I.A surfactant’s equilibrium spreading pressure (ESP) is the maximum decrease in surface tension achievable at equilibrium below the Krafft point. Difficulties in measuring the ESP have been noted previously but no well-established experimental protocols to overcome them exist. We present a case study of three solid amphiphiles with different propensities to spread on the air–water interface. Starting with the partially water soluble n-dodecanol (C12H25OH), which spreads instantaneously. The strong Marangoni flows associated with the spreading result in the dislocating of the Wilhelmy plate or crystals attaching to it. A temporary mechanical barrier in front of the spreading crystals mitigates the flows disturbing the plate. Presaturating the subphase with the amphiphile prevents the establishment of dynamic steady states, reduces the standard error by a factor of three and causes faster equilibration. The perfluoroalkylated analog of dodecanol (11:1 fluorotelomer alcohol, C11F23CH2OH) is slow spreading. With surfactant crystals on the interface, the surface pressure reaches a pre-equilibrium plateau within an hour, followed by equilibration on day-long timescales. We show that it is better to estimate the ESP by averaging the values of multiple pre-equilibrium plateaus rather than waiting for equilibrium to be established. Finally, the nonspreading amphiphile DPPC exhibits a large barrier for the mass transfer from the DPPC crystal to the aqueous surface. This was overcome by introducing a volatile, water-immiscible solvent deposited on the surface next to the crystals to facilitate the spreading process and leave behind a monolayer.Item On the Influence of the Ionization-Recombination Processes on the Hydrogen Plasma Polytropic Index(2021-07-20) Mishonov T.M.; Dimitrova I.M.; Varonov A.M.An analytical approximation for the polytropic index of a hydrogen gas has been derived. The derived expressions can be useful for theoretical work and numerical calculations. These results open the possibility of direct computation of these thermodynamic quantities, rather than interpolating from tables. Additionally, the polytropic index is graphically represented as a function of temperature and density. It is concluded that the partially ionized hydrogen plasma cannot be exactly polytropic. The calculated deviations from the monoatomic value 5/3 are significant and measurable. The present theory supposes that hydrogen molecules are completely dissociated, and this analytical result for pure hydrogen plasma can be applied for the solar chromosphere, where He ionization is negligible and H2 dissociation is almost complete. These two conditions define the ranges of applicability of temperatures and densities. The analytical result for pure hydrogen plasma is a test example of how this approach can be extended for an arbitrary gas cocktail.Item Probability distribution function of crossover frequency of operational amplifiers(2021-07-01) Mishonov T.M.; Petkov E.G.; Dimitrova I.M.; Serafimov N.S.; Varonov A.M.For the first time the cumulative distribution function and histogram of the crossover frequency of a contemporary operational amplifier ADA4898-2 is experimentally studied. Using a USB lock–in amplifier, which allows automatic frequency sweep of the current response of a non-inverting amplifier with significant static amplification, we measure the crossover frequency of 200 samples of ADA4898-2 operational amplifiers. This new method gives a significant advantage in accuracy and speed of study of every operational amplifier. The theory we use is based on the universal relation between time dependent output and input voltages. This common relation for all operational amplifiers is applicable for frequencies much smaller than the crossover frequency and the frequencies of non-dominant poles. In other words, this approximation is adequate, when an operational amplifier is included in a circuit with significant amplification.Item Quadrupolarizability of liquid mixtures(2020-12-24) Dimitrova I.M.; Yordanova V.I.; Slavchov R.I.Theoretical expressions for the macroscopic polarizability and quadrupolarizability of a quadrupolar mixture are derived. The theory is demonstrated on the example of a liquid mixture of methane and nitrogen (nonquadrupolar plus quadrupolar component). It turns out that the dielectric permittivity (the “dipole strength” of the liquid) of this mixture changes little with the composition, while the quadrupolar length (“quadrupolar strength”) almost triples as the fraction of nitrogen approaches one. A set of such mixtures can be used as standard quadrupolar solvents to study systematically phenomena such as quadrupolar solvatochromism, the effect of the solvent on the rate of a reaction etc.Item Simple do-it-yourself experimental set-up for electron charge qe measurement(2018-08-29) Mishonov T.M.; Petkov E.G.; Mihailova N.Z.; Stefanov A.A.; Dimitrova I.M.; Gourev V.N.; Serafimov N.S.; Danchev V.I.; Varonov A.M.A simple experiment for the electron charge q e measurement is described. The experimental set-up contains standard electronic equipment only and can be built in every high-school lab all around the world with several days' pocket money budget. It is concluded that it is time such a practice should be included in regular high-school education. The achieved 13% accuracy is comparable to the best student university labs. The measurement is based on Schottky noise generated by a photodiode. Using a criterion of dollar-per-accuracy for the electron charge q e measurement, this is definitely the world's best educational experiment. An industrial replica can easily be sold across the globe.Item Sound absorption in partially ionized hydrogen plasma and heating mechanism of solar chromosphere(2021-02-01) Mishonov T.M.; Dimitrova I.M.; Varonov A.M.The temperature dependence of rates of electron impact ionization and two electrons recombination are calculated using Wannier cross section of electron impact ionization of neutral hydrogen atom. Entropy production and power dissipation are derived for the case when the ionization degree deviates from its equilibrium value. This is the special case of the obtained general formula for entropy production accompanying chemical reactions. Damping rate of the sound waves is calculated and the conditions when ionization processes dominate are considered. A quasi-classical approximation for the heating mechanism of solar chromosphere is proposed. Several analogous phenomena for damping rates in liquids and crystals are shortly discussed, for example, deaf sound of a glass of beer or English salt solution. An explicit expression for the second or bulk (or volume) viscosity of hydrogen plasma is calculated from firsts principles. For the first time some second viscosity is calculated from first principles.Item The cause of accelerated desorption of sparingly soluble dodecanol monolayers: Convection or leakage?(2021-11-20) Minkov I.L.; Dimitrova I.M.; Arabadzhieva D.; Mileva E.; Slavchov R.I.The dissolution of sparingly soluble surfactants from spread monolayers is a complex multi-staged process. The desorption of dodecanol from the surface of water follows mixed barrier/diffusion kinetics only in the first stages of the dissolution. Significant acceleration of the desorption has been observed experimentally after this initial period, which has been hypothesized to be due to onset of convective diffusion; the source of convection, however, has never been identified. The goal of this work is to investigate the question through desorption experiments under controlled convection and respective modeling of the process under mixed barrier/convective diffusion control. Several hypotheses for the cause of the accelerated desorption have been tested. The analysis has shown that natural convection, Marangoni convection, convection due to the motion of the mechanical barrier of the Langmuir trough, and artificial convection caused by an electromagnetic stirrer cannot produce desorption rates of the observed magnitude. These findings convincingly prove for the first time that the convective diffusion has less of a role in the transport process than previously thought. The most likely reason for the acceleration is identified as leakage through the movable barrier. The rate of this leakage is estimated form the experimental data. Implications for the use of adsorption isobars to study desorption kinetics are discussed.Item The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential(2015-10-21) Slavchov R.I.; Dimitrova I.M.; Ivanov T.The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension - of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of the bulk phases and the intrinsic polarization of the interface. The coefficient of the dielectro-Marangoni effect (surface flow due to gradient of the normal electric field) is found. A model of the Langevin type for the surface dipole moment and the intrinsic surface polarizability is presented.Item Tunable high-Q resonator by general impedance converter(2021-02-01) Mifune T.; Mishonov T.M.; Serafimov N.S.; Dimitrova I.M.; Popeski-Dimovski R.; Velkoska L.; Petkov E.G.; Varonov A.M.; Barone A.A tunable high-Q resonator is performed in the schematics of the General Impedance Converter (GIC). In the framework of frequency dependent open-loop gain of operational amplifiers, a general formula of the frequency dependence of the impedance of GIC is derived. The explicit formulas for the resonance frequency and Q-factor include as an immanent parameter the crossover frequency of the operational amplifier. Voltage measurements of GIC with a lock-in amplifier perfectly agree with the derived formulas.