Entropy as a measure of diffusion

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.     

A meshless method for solving an inverse spacewise-dependent heat source problem

In this paper an effective meshless and integration-free numerical scheme for solving an inverse spacewise-dependent heat source problem is proposed. Due to the use of the fundamental solution as basis functions, the method leads to a global approximation scheme in both spatial and time domains. The standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations. The effectiveness of the algorithm is illustrated by several numerical examples.     

Method of solving the inverse spectral problem

We describe a method of solving the inverse spectral problem which is applicable to free molecules as well as to molecules in a medium. We give a criterion for the uniqueness of the definition of the force matrix. This criterion links the necessary number of normal proper vibrations of a molecule with a number of necessary form parameters. We calculate the force matrix of tetrahedral molecules CH₄, CD₄, and CT₄. When we use zero-point values for frequencies of normal vibrations the relative discrepancy in the corresponding force-matrix elements does not exceed 0.3%.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–57, April, 1987.     

The inverse problem for diffusion equations

In the standard procedure one has to find the concentration from given initial (and boundary) conditions. We investigate here an inverse problem: to find the initial concentration from the known resulting concentration. This problem is of importance particularly for non-linear diffusion equations where the concentration dependenceD D(c) of the diffusion coefficient is analysed in terms of the Boltzmann-like solutionc f(xt^–1/2). This type of solution is, however, closely related to a very special initial condition for the concentration. The disregard of this fact might lead to misleading analysis ofD(c).     

Supersymmetric Yang-Mills equations as an inverse scattering problem

The equations of motion (for N=3, 4) and the constraint equations (N=1, 2) for supersymmetric Yang-Mills theories are shown to be the compatibility conditions of some system of linear equations with a parameter.     

The I2(B) predissociation by solving an inverse atoms-in-molecule problem

The valence electronic states of the iodine molecule are analysed by means of a simple atoms-in-molecule model which accounts for the lowest ²P states of iodine atoms and approximates the spin-orbit interaction by its atomic part. For this model, an inverse problem is solved, i.e. non-relativistic potential energy curves and diabatic couplings are determined by a least-squares fit to known relativistic potential energy curves. The resulting adiabatic wave functions are used to calculate the electronic matrix elements responsible for natural, hyperfine and magnetic predissociation of the iodine molecule in the B0⁺ _u: state. The results are in reasonable agreement with experimental data, being stable enough with respect to the variation of input relativistic potentials. They also indicate the importance of diabatic couplings between the non-relativistic states of the same symmetry.     

Algorithm for solving the inverse problem of ballistics in the case of an asymmetric object

An algorithm to identify the aerodynamic characteristics of an asymmetric object from its trajectory data obtained in a ballistic experiment is developed based on the technique for estimating the nonlinear system’s parameters. Using the method of successive approximations, the coefficients of the aerodynamic function polynomial representation are found that best describe measuring data. The essence of the algorithm is the solution of the direct problem of the symmetric object’s dynamics using the complete set of Euler dynamic equations. The variation of the desired parameters is statistically estimated during calculations. The algorithm allows for jointly processing data of a series of experiments with similar models. Thereby, the volume of processed data is augmented and the final result becomes more accurate.     

Manipulation with heterogeneity within a species population formulated as an inverse problem

Dependence of the evolutionary dynamics on the population’s heterogeneity has been reliably recognized and studied within the frame of evolutionary optimization theory. As the causal relation between the heterogeneity and dynamics of environment has been revealed, the possibility to influence convergence rate of evolutionary processes by purposeful manipulation with environment emerges.For the above purposes we formulate the task as the inverse problem meaning that desired population heterogeneity, quantified by Tsallis information entropy, represents the model’s input and dynamics of environment leading to desired population heterogeneity is looked for. Here the presented abstract model of evolutionary motion within the inverse model of replicating species is case-independent and it is relevant for the broad range of phenomena observed at cellular, ecological, economic and social scales. We envision relevance of the model for anticancer therapy, in which the effort is to circumvent heterogeneity as it typically correlates with the therapy efficiency.     

Upper bound of errors in solving the inverse problem of identifying a voice source

The paper considers the inverse problem of finding the shape of a voice-source pulse from a specified segment of a speech signal using a special mathematical model that relates these quantities. A variational method for solving the formulated inverse problem for two new parametric classes of sources is proposed: a piecewise-linear source and an A-source. The error in the obtained approximate solutions of the inverse problem is considered, and a technique to numerically estimate this error is proposed, which is based on the theory of a posteriori estimates of the accuracy in solving ill-posed problems. A computer study of the adequacy of the proposed models of sources, and a study of the a posteriori estimates of the accuracy in solving inverse problems for such sources were performed using various types of voice signals. Numerical experiments for speech signals showed satisfactory properties of such a posteriori estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes for the investigated speech material is on average ~7%. It is noted that the a posteriori accuracy estimates can be used as a criterion for the quality of determining the voice-source pulse shape in the speaker-identification problem.     

Perturbation method for solving the inverse vibrational problem in dependent coordinates

Solution of the inverse vibrational problem (IVP) when the dependent coordinates are excluded leads to a linear combination of the molecular force constants, of very limited usefulness for a series of related compounds. In this work we consider the question of separating these combinations during the solution of the IVP in a system of dependent coordinates. Such a solution is obtained by introducing a perturbation into the matrix of kinematic coefficients with the help of a certain self-consistent matrix. We obtain intrinsic force constants for tetrahedral hydrides (methane, silane, and germane) which reproduce experimental frequency spectra well.Three Hundredth Anniversary of the Reunion of the Ukraine with Russia State University, DnepropetrovskTranslated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1987.     

SUSY at the ILC and solving the LHC inverse problem

Recently a large-scale study of points in the MSSM parameter space which are problematic at the Large Hadron Collider (LHC) has been performed. This work was carried out in part to determine whether the proposed International Linear Collider (ILC) could be used to solve the LHC inverse problem. The results suggest that while the ILC will be a valuable tool, an energy upgrade may be crucial to its success, and that, in general, precision studies of the MSSM are more difficult at the ILC than has generally been believed.     

On an inverse spectral problem

We study an inverse spectral problem for the Sturm–Liouville problem. Such a problem arises in the study of micro- and nano-rods.     

Entropy production in a cell and reversal of entropy flow as an anticancer therapy

The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and lowintensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently reverse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the biological tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful information from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.      

Calculation of transport coefficient profiles in modulation experiments as an inverse problem

The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial approach, is proposed for periodically modulated experiments, within the context of the standard advection-diffusion model where these issues are related to the vanishing of the determinant of a 2×2 matrix. This sheds light on the accuracy of calculations with transport codes, and provides a path for a more precise assessment of the profiles and of the related uncertainty.     

Yang-Mills equations as inverse scattering problem

Non-linear self-duality equations are shown to be conditions of compatibility of two linear equations. All the N-instanton fields are constructed explicitly.     

Variational iteration method for solving an inverse parabolic equation

The variational iteration method is applied to solving an inverse problem of determining an unknown parameter in a linear parabolic equation. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. We get a rapid convergent sequence tending to the exact solution of the inverse problem. To show the efficiency of the present method, some interesting examples are presented.     

On an inverse problem in quantum statistical physics

Restoration of the full probability distribution by means of its asymptotics is considered. In the present contribution such cases are discussed where information about the asymptotics can be deduced from statistical properties of real physical systems represented, e.g., by light beams in the case of the photoproduction of electrons in the field of quantum optics or by (charged) secondaries produced by collisions observed in the field of high energy physics. Arbitrarily many modes with superposition of stochastic and coherent components are taken into account including also the case of pure coherent fields. The difference of the last case compared with the superposition alone is emphasized. To solve the corresponding inverse problems the Poisson transform is applied. Scaling properties of asymptotic probability distributions and some open problems are mentioned too.     

Solution of an inverse problem in scattering theory

Hoyt (1939) and Firsov devised methods in classical mechanics to deduce a central scattering potential from a measured differential effective cross-section in the nonrelativistic case. These methods are here extended to the relativistic case. A detailed analysis of the applicability of all methods has been undertaken for potentials of the form V(r) = ±r^–k for sufficiently high energies of the colliding particles. It is found that Hoyt's method is inapplicable in the relativistic case only when the potential represents attraction. A relatively simple method is given for deducing the parameters and k for a monotonic attraction potential that can be approximated by V(r) = –r^–k. The method is based on simple arguments concerning the dimensions of the cross-section. It is sufficient to know only two values of the integral cross-section in the same range of angles but at different energies to determine the parameters.