Universal behaviour of ideal and interacting quantum gases in two dimensions

I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the microscopic exclusion statistics, nor on the interaction. Such systems are called {\em thermodynamically equivalent} and I show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems. This provides a method, different from the bosonisation technique, to transform between systems of different exclusion statistics. In the last section the macroscopic aspects of this method are discussed. In Appendix A I calculate the fluctuation of the ground state population of a condensed Bose gas in grandcanonical ensemble and mean field approximation, while in Appendix B I show a situation where although the system exhibits fractional exclusion properties on microscopic energy intervals, a rigorous calculation of the population of single particle states reveals a condensation phenomenon. This also implies a malfunction of the usual and simplified calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the original submission I just mentioned the condensation, which is now detailed in Appendix B. They were intended for a separate paper. Reason for changes: rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge

Development of the algorithm for aircraft control at inaccurate measurement of the state vector and variable accuracy parameter

A parametric method of the synthesis of control in the closed circuit, taking into account explicitly generalized error of the inertial module, is presented. The law of control in the form of analytical formulas is typically assigned to the control program and does not change during flight of an unmanned aerial vehicle. This decreases the capabilities of the autonomous flight control system to overcome control errors, which occur for various reasons. To verify assumptions about a possibility of improving the accuracy of an aerial vehicle control by the data of the strapdown inertial navigation system on a certain time interval of autonomous operation, the calculation experiment was conducted with the use of the developed software complex, simulating operation of the automatic flight control system. Parametrization of the law of control is considered as the main contribution (the outcome). Introduction of the parameter made it possible to decrease a negative impact of measurement errors and other disturbing factors on accuracy of reaching by the point of flight destination. Through computer modeling, it was shown that it is possible to decrease the impact of a generalized measurement error on generation of values of control functions by changing the value of the parameter. Analytical expressions for the estimation of accuracy of automatic control at the known generalized error of the inertial module and limited disturbing influences were obtained. After analyzing the influence of these factors on accuracy of the object control, a set of recommendations on selection of a variable parameter of synthesis of control depending on precision level of the sensors, used in the inertial module of measuring sensors, was generated.Розглянуто розв’язання термінальної задачі управління та синтезований параметризований закон управління в аналітичному вигляді, який залежить від змінного параметра глибини прогнозу. Досліджено особливості впливу величини параметра управління на точність досягнення кінцевої точки, дані рекомендації з вибору параметра для нівелювання помилки інерційних вимірювань. Синтез управління здійснюється методом переслідування ведучої точки за інформацією, отриманою інтегруванням вимірювань фактичного прискорення і містить помилку, характерну для акселерометрів

Surface Impedance Determination via Numerical Resolution of the Inverse Helmholtz Problem

Assigning boundary conditions, such as acoustic impedance, to the frequency domain thermoviscous wave equations (TWE), derived from the linearized Navier-Stokes equations (LNSE) poses a Helmholtz problem, solution to which yields a discrete set of complex eigenfunctions and eigenvalue pairs. The proposed method -- the inverse Helmholtz solver (iHS) -- reverses such procedure by returning the value of acoustic impedance at one or more unknown impedance boundaries (IBs) of a given domain, via spatial integration of the TWE for a given real-valued frequency with assigned conditions on other boundaries. The iHS procedure is applied to a second-order spatial discretization of the TWEs on an unstructured staggered grid arrangement. Only the momentum equation is extended to the center of each IB face where pressure and velocity components are co-located and treated as unknowns. The iHS is finally closed via assignment of the surface gradient of pressure phase over the IBs, corresponding to assigning the shape of the acoustic waveform at the IB. The iHS procedure can be carried out independently for different frequencies, making it embarrassingly parallel, and able to return the complete broadband complex impedance distribution at the IBs in any desired frequency range to arbitrary numerical precision. The iHS approach is first validated against Rott's theory for viscous rectangular and circular ducts. The impedance of a toy porous cavity with a complex geometry is then reconstructed and validated with companion fully compressible unstructured Navier-Stokes simulations resolving the cavity geometry. Verification against one-dimensional impedance test tube calculations based on time-domain impedance boundary conditions (TDIBC) is also carried out. Finally, results from a preliminary analysis of a thermoacoustically unstable cavity are presented.Comment: As submitted to AIAA Aviation 201

Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles

We give two formulations of exclusion statistics (ES) using a variable number of bosonic or fermionic single-particle states which depend on the number of particles in the system. Associated bosonic and fermionic ES parameters are introduced and are discussed for FQHE quasiparticles, anyons in the lowest Landau level and for the Calogero-Sutherland model. In the latter case, only one family of solutions is emphasized to be sufficient to recover ES; appropriate families are specified for a number of formulations of the Calogero-Sutherland model. We extend the picture of variable number of single-particle states to generalized ideal gases with statistical interaction between particles of different momenta. Integral equations are derived which determine the momentum distribution for single-particle states and distribution of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE