Ruslan Davidchack | University of Leicester (original) (raw)

Papers by Ruslan Davidchack

Research paper thumbnail of Weighted-density approximation for general nonuniform fluid mixtures

Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, Mar 10, 1999

In order to construct a general density-functional theory for nonuniform fluid mixtures, we propo... more In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)]. This extension corrects a deficiency in a similar extension proposed earlier by Denton and Ashcroft [Phys. Rev. A 42, 7312 (1990)], in that that functional cannot be applied to the multicomponent nonuniform fluid systems with spatially varying composition, such as solid-fluid interfaces. As a test of the accuracy of our functional, we apply it to the calculation of the freezing phase diagram of a binary hard-sphere fluid, and compare the results to simulation and the Denton-Ashcroft extension.

Research paper thumbnail of Parameterising the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

Http Dx Doi Org 10 1080 00268976 2014 986240, Dec 10, 2014

The inhomogeneous structure of a fluid at a wall can be characterised in several ways. Within a t... more The inhomogeneous structure of a fluid at a wall can be characterised in several ways. Within a thermodynamic description, the surface free energy γ and the excess adsorption Γ are of central importance. For theoretical studies, closed expression of γ and Γ can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for γ and Γ, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for γ and Γ to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterisations show significant deviation at high density. In this work, we propose new parameterisations for γ and Γ that agree with the simulation data within statistical error over the entire fluid density range.

Research paper thumbnail of Fast communication Adaptive approximation of feedback rank %lters for continuous signals

Rank-based nonlinear %ltering techniques are steadily gaining in popularity due to their robustne... more Rank-based nonlinear %ltering techniques are steadily gaining in popularity due to their robustness. However, the analog implementation of these techniques meets with considerable conceptual and practical di2culties. Here we describe an adaptive approximation for a rank %lter of a continuous signal expressed in terms of a system of di3erential equations easily implementable in an analog circuit. The design is based on consideration of the %nite precision of physical measurements, which leads to simple and e2cient implementation of many traditionally digital analysis tools. We also illustrate the performance of the adaptive approximation %lter in comparison with the respective 'exact' rank %lter in a boxcar moving window.

Research paper thumbnail of Theory and Simulation of Hard Sphere Crystal-Melt Interfaces

Research paper thumbnail of Conditions for the Existence of Half-Integer Quantum Flux in a Tricrystal Junction

Research paper thumbnail of Theory and Simulation of Binary Hard Sphere Solid-Liquid Interface

Research paper thumbnail of Normal-State Transport Properties of Cuprate Superconductors: Evidence for Mixed-Charge State

Research paper thumbnail of Mixed-Charge State in Superconductors

Research paper thumbnail of A Simple Superconducting Mixed-Charge Quantized Flux Hall Effect Model

Based on a single gauge invariance for a mixed charge superconducting condensate [K. W. Wong and ... more Based on a single gauge invariance for a mixed charge superconducting condensate [K. W. Wong and R. L. Davidchack, Phys. Lett. A 208, 171 (1995)] a simple model for the Hall effect on the quantized fluxoids gives properties consistent with experimental observations including the change of sign of Hall resistivity when temperature decreases through the transition region (the possibility of three sign changes is predicted) and the scaling power relationship between rho_xx, the diagonal resistivity, and rho_xy, the Hall resistivity.

Research paper thumbnail of Anisotropic free energies of crystal-melt interfaces

Recently, there have been significant advances in approaches to calculating the free energy of cr... more Recently, there have been significant advances in approaches to calculating the free energy of crystal-melt interfaces from simulations. Current approaches can not only predict accurate values, but can resolve the anisotropies in the values on the order of 1-2%. We demonstrate these approaches, in particular the fluctuation approach applicable to rough interfaces, and compare the results. For the Lennard-Jones system,

Research paper thumbnail of Blind Adaptive Analog Nonlinear Filters for Noise Mitigation in Powerline Communication Systems

Research paper thumbnail of Parameterising the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

Molecular Physics, 2014

ABSTRACT he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Wi... more ABSTRACT he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy gamma\gammagamma and the excess adsorption Gamma\GammaGamma are of central importance. For theoretical studies closed expression of gamma\gammagamma and Gamma\GammaGamma can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for gamma\gammagamma and Gamma\GammaGamma, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for gamma\gammagamma and Gamma\GammaGamma to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterizations show significant deviation at high density. In this work, we propose new parameterizations for gamma\gammagamma and Gamma\GammaGamma that agree with the simulation data within statistical error over the entire fluid density range.

Research paper thumbnail of Out-of-band and adjacent-channel interference reduction by analog nonlinear filters

EURASIP Journal on Advances in Signal Processing, 2015

In a perfect world, we would have 'brick wall' filters, no-distortion amplifiers and mixers, and ... more In a perfect world, we would have 'brick wall' filters, no-distortion amplifiers and mixers, and well-coordinated spectrum operations. The real world, however, is prone to various types of unintentional and intentional interference of technogenic (man-made) origin that can disrupt critical communication systems. In this paper, we introduce a methodology for mitigating technogenic interference in communication channels by analog nonlinear filters, with an emphasis on the mitigation of out-of-band and adjacent-channel interference. Interference induced in a communications receiver by external transmitters can be viewed as wide-band non-Gaussian noise affecting a narrower-band signal of interest. This noise may contain a strong component within the receiver passband, which may dominate over the thermal noise. While the total wide-band interference seen by the receiver may or may not be impulsive, we demonstrate that the interfering component due to power emitted by the transmitter into the receiver channel is likely to appear impulsive under a wide range of conditions. We give an example of mechanisms of impulsive interference in digital communication systems resulting from the nonsmooth nature of any physically realizable modulation scheme for transmission of a digital (discontinuous) message. We show that impulsive interference can be effectively mitigated by nonlinear differential limiters (NDLs). An NDL can be configured to behave linearly when the input signal does not contain outliers. When outliers are encountered, the nonlinear response of the NDL limits the magnitude of the respective outliers in the output signal. The signal quality is improved in excess of that achievable by the respective linear filter, increasing the capacity of a communications channel. The behavior of an NDL, and its degree of nonlinearity, is controlled by a single parameter in a manner that enables significantly better overall suppression of the noise-containing impulsive components compared to the respective linear filter. Adaptive configurations of NDLs are similarly controlled by a single parameter and are suitable for improving quality of nonstationary signals under time-varying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems and to be used as an enhancement, or as a low-cost alternative, to the state-of-art interference mitigation methods.

Research paper thumbnail of Adaptive Analog Nonlinear Algorithms and Circuits for Improving Signal Quality in the Presence of Technogenic Interference

MILCOM 2013 - 2013 IEEE Military Communications Conference, 2013

We introduce algorithms and conceptual circuits for Nonlinear Differential Limiters (NDLs), and o... more We introduce algorithms and conceptual circuits for Nonlinear Differential Limiters (NDLs), and outline a methodology for their use to mitigate in-band noise and interference, especially that of technogenic (man-made) origin, affecting various real, complex, and/or vector signals of interest, and limiting the performance of the affected devices and services. At any given frequency, a linear filter affects both the noise and the signal of interest proportionally, and when a linear filter is used to suppress the interference outside of the passband of interest, the resulting signal quality is invariant to the type of the amplitude distribution of the interfering signal, as long as the total power and the spectral composition of the interference remain unchanged. Such a linear filter can be converted into an NDL by introducing an appropriately chosen feedback-based nonlinearity into the response of the filter, and the NDL may reduce the spectral density of particular types of interferences in the signal passband without significantly affecting the signal of interest. As a result, the signal quality can be improved in excess of that achievable by the respective linear filter. The behavior of an NDL filter and its degree of nonlinearity is controlled by a single parameter in a manner that enables significantly better overall suppression of the noise compared to the respective linear filter, especially when the noise contains components of technogenic origin. Adaptive configurations of NDLs are similarly controlled by a single parameter, and are suitable for improving quality of non-stationary signals under time-varying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems, and to be used as an enhancement, or as a low-cost alternative, to the state-of-art interference mitigation methods.

Research paper thumbnail of Weighted-density approximation for general nonuniform fluid mixtures

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

In order to construct a general density-functional theory for nonuniform fluid mixtures, we propo... more In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)]. This extension corrects a deficiency in a similar extension proposed earlier by Denton and Ashcroft [Phys. Rev. A 42, 7312 (1990)], in that that functional cannot be applied to the multicomponent nonuniform fluid systems with spatially varying composition, such as solid-fluid interfaces. As a test of the accuracy of our functional, we apply it to the calculation of the freezing phase diagram of a binary hard-sphere fluid, and compare the results to simulation and the Denton-Ashcroft extension.

Research paper thumbnail of Simulation of the binary hard-sphere crystal/melt interface

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1996

Simulation of the binary hard-sphere crystal/melt interface. Ruslan L. Davidchack and Brian B. La... more Simulation of the binary hard-sphere crystal/melt interface. Ruslan L. Davidchack and Brian B. Laird Department of Chemistry, University of Kansas, Lawrence, Kansas 66045. Received 5 June 1996 We report results of molecular ...

Research paper thumbnail of Numerical Mathematics and Advanced Applications - ENUMATH 2013

Lecture Notes in Computational Science and Engineering, 2015

... 381 A Multiresolution Method for the Simulation of Sedimentation-Consolidation Processes Raim... more ... 381 A Multiresolution Method for the Simulation of Sedimentation-Consolidation Processes Raimund Burger, Alice Kozakevicius ... Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method Daniele Boffi, Lucia Gastaldi, Luca ...

Research paper thumbnail of Adaptive approximation of feedback rank filters for continuous signals

Signal Processing, 2004

Rank-based nonlinear ÿltering techniques are steadily gaining in popularity due to their robustne... more Rank-based nonlinear ÿltering techniques are steadily gaining in popularity due to their robustness. However, the analog implementation of these techniques meets with considerable conceptual and practical di culties. Here we describe an adaptive approximation for a rank ÿlter of a continuous signal expressed in terms of a system of di erential equations easily implementable in an analog circuit. The design is based on consideration of the ÿnite precision of physical measurements, which leads to simple and e cient implementation of many traditionally digital analysis tools. We also illustrate the performance of the adaptive approximation ÿlter in comparison with the respective 'exact' rank ÿlter in a boxcar moving window.

Research paper thumbnail of Efficient Detection of Periodic Orbits in Chaotic Systems by Stabilizing Transformations

SIAM Journal on Scientific Computing, 2006

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-... more An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp. 4733-4736] with a modified semi-implicit Euler iterative scheme and seeding with periodic orbits of neighbouring periods, has been shown to be highly efficient when applied to low-dimensional systems. The difficulty in applying the algorithm to higher-dimensional systems is mainly due to the fact that the number of the stabilising transformations grows extremely fast with increasing system dimension. Here we analyse the properties of stabilising transformations and propose an alternative approach for constructing a smaller set of transformations. The performance of the new approach is illustrated on the four-dimensional kicked double rotor map and the six-dimensional system of three coupled Hénon maps.

Research paper thumbnail of Signal analysis through analog representation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003

We present an approach to the analysis of signals based on analog representation of measurements.... more We present an approach to the analysis of signals based on analog representation of measurements. Methodologically, it relies on the consideration and full use of the continuous nature of a realistic, as opposed to an idealized, measuring process. Mathematically, it is based on the transformation of discrete or continuous signals into normalized continuous scalar fields with the mathematical properties of distribution functions. This approach allows a simple and efficient implementation of many traditionally digital analysis tools, including nonlinear filtering techniques based on order statistics. It also enables the introduction of a large variety of new characteristics of both one- and multi-dimensional signals, which have no digital counterparts.

Research paper thumbnail of Weighted-density approximation for general nonuniform fluid mixtures

Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, Mar 10, 1999

In order to construct a general density-functional theory for nonuniform fluid mixtures, we propo... more In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)]. This extension corrects a deficiency in a similar extension proposed earlier by Denton and Ashcroft [Phys. Rev. A 42, 7312 (1990)], in that that functional cannot be applied to the multicomponent nonuniform fluid systems with spatially varying composition, such as solid-fluid interfaces. As a test of the accuracy of our functional, we apply it to the calculation of the freezing phase diagram of a binary hard-sphere fluid, and compare the results to simulation and the Denton-Ashcroft extension.

Research paper thumbnail of Parameterising the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

Http Dx Doi Org 10 1080 00268976 2014 986240, Dec 10, 2014

The inhomogeneous structure of a fluid at a wall can be characterised in several ways. Within a t... more The inhomogeneous structure of a fluid at a wall can be characterised in several ways. Within a thermodynamic description, the surface free energy γ and the excess adsorption Γ are of central importance. For theoretical studies, closed expression of γ and Γ can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for γ and Γ, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for γ and Γ to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterisations show significant deviation at high density. In this work, we propose new parameterisations for γ and Γ that agree with the simulation data within statistical error over the entire fluid density range.

Research paper thumbnail of Fast communication Adaptive approximation of feedback rank %lters for continuous signals

Rank-based nonlinear %ltering techniques are steadily gaining in popularity due to their robustne... more Rank-based nonlinear %ltering techniques are steadily gaining in popularity due to their robustness. However, the analog implementation of these techniques meets with considerable conceptual and practical di2culties. Here we describe an adaptive approximation for a rank %lter of a continuous signal expressed in terms of a system of di3erential equations easily implementable in an analog circuit. The design is based on consideration of the %nite precision of physical measurements, which leads to simple and e2cient implementation of many traditionally digital analysis tools. We also illustrate the performance of the adaptive approximation %lter in comparison with the respective 'exact' rank %lter in a boxcar moving window.

Research paper thumbnail of Theory and Simulation of Hard Sphere Crystal-Melt Interfaces

Research paper thumbnail of Conditions for the Existence of Half-Integer Quantum Flux in a Tricrystal Junction

Research paper thumbnail of Theory and Simulation of Binary Hard Sphere Solid-Liquid Interface

Research paper thumbnail of Normal-State Transport Properties of Cuprate Superconductors: Evidence for Mixed-Charge State

Research paper thumbnail of Mixed-Charge State in Superconductors

Research paper thumbnail of A Simple Superconducting Mixed-Charge Quantized Flux Hall Effect Model

Based on a single gauge invariance for a mixed charge superconducting condensate [K. W. Wong and ... more Based on a single gauge invariance for a mixed charge superconducting condensate [K. W. Wong and R. L. Davidchack, Phys. Lett. A 208, 171 (1995)] a simple model for the Hall effect on the quantized fluxoids gives properties consistent with experimental observations including the change of sign of Hall resistivity when temperature decreases through the transition region (the possibility of three sign changes is predicted) and the scaling power relationship between rho_xx, the diagonal resistivity, and rho_xy, the Hall resistivity.

Research paper thumbnail of Anisotropic free energies of crystal-melt interfaces

Recently, there have been significant advances in approaches to calculating the free energy of cr... more Recently, there have been significant advances in approaches to calculating the free energy of crystal-melt interfaces from simulations. Current approaches can not only predict accurate values, but can resolve the anisotropies in the values on the order of 1-2%. We demonstrate these approaches, in particular the fluctuation approach applicable to rough interfaces, and compare the results. For the Lennard-Jones system,

Research paper thumbnail of Blind Adaptive Analog Nonlinear Filters for Noise Mitigation in Powerline Communication Systems

Research paper thumbnail of Parameterising the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

Molecular Physics, 2014

ABSTRACT he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Wi... more ABSTRACT he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy gamma\gammagamma and the excess adsorption Gamma\GammaGamma are of central importance. For theoretical studies closed expression of gamma\gammagamma and Gamma\GammaGamma can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for gamma\gammagamma and Gamma\GammaGamma, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for gamma\gammagamma and Gamma\GammaGamma to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterizations show significant deviation at high density. In this work, we propose new parameterizations for gamma\gammagamma and Gamma\GammaGamma that agree with the simulation data within statistical error over the entire fluid density range.

Research paper thumbnail of Out-of-band and adjacent-channel interference reduction by analog nonlinear filters

EURASIP Journal on Advances in Signal Processing, 2015

In a perfect world, we would have 'brick wall' filters, no-distortion amplifiers and mixers, and ... more In a perfect world, we would have 'brick wall' filters, no-distortion amplifiers and mixers, and well-coordinated spectrum operations. The real world, however, is prone to various types of unintentional and intentional interference of technogenic (man-made) origin that can disrupt critical communication systems. In this paper, we introduce a methodology for mitigating technogenic interference in communication channels by analog nonlinear filters, with an emphasis on the mitigation of out-of-band and adjacent-channel interference. Interference induced in a communications receiver by external transmitters can be viewed as wide-band non-Gaussian noise affecting a narrower-band signal of interest. This noise may contain a strong component within the receiver passband, which may dominate over the thermal noise. While the total wide-band interference seen by the receiver may or may not be impulsive, we demonstrate that the interfering component due to power emitted by the transmitter into the receiver channel is likely to appear impulsive under a wide range of conditions. We give an example of mechanisms of impulsive interference in digital communication systems resulting from the nonsmooth nature of any physically realizable modulation scheme for transmission of a digital (discontinuous) message. We show that impulsive interference can be effectively mitigated by nonlinear differential limiters (NDLs). An NDL can be configured to behave linearly when the input signal does not contain outliers. When outliers are encountered, the nonlinear response of the NDL limits the magnitude of the respective outliers in the output signal. The signal quality is improved in excess of that achievable by the respective linear filter, increasing the capacity of a communications channel. The behavior of an NDL, and its degree of nonlinearity, is controlled by a single parameter in a manner that enables significantly better overall suppression of the noise-containing impulsive components compared to the respective linear filter. Adaptive configurations of NDLs are similarly controlled by a single parameter and are suitable for improving quality of nonstationary signals under time-varying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems and to be used as an enhancement, or as a low-cost alternative, to the state-of-art interference mitigation methods.

Research paper thumbnail of Adaptive Analog Nonlinear Algorithms and Circuits for Improving Signal Quality in the Presence of Technogenic Interference

MILCOM 2013 - 2013 IEEE Military Communications Conference, 2013

We introduce algorithms and conceptual circuits for Nonlinear Differential Limiters (NDLs), and o... more We introduce algorithms and conceptual circuits for Nonlinear Differential Limiters (NDLs), and outline a methodology for their use to mitigate in-band noise and interference, especially that of technogenic (man-made) origin, affecting various real, complex, and/or vector signals of interest, and limiting the performance of the affected devices and services. At any given frequency, a linear filter affects both the noise and the signal of interest proportionally, and when a linear filter is used to suppress the interference outside of the passband of interest, the resulting signal quality is invariant to the type of the amplitude distribution of the interfering signal, as long as the total power and the spectral composition of the interference remain unchanged. Such a linear filter can be converted into an NDL by introducing an appropriately chosen feedback-based nonlinearity into the response of the filter, and the NDL may reduce the spectral density of particular types of interferences in the signal passband without significantly affecting the signal of interest. As a result, the signal quality can be improved in excess of that achievable by the respective linear filter. The behavior of an NDL filter and its degree of nonlinearity is controlled by a single parameter in a manner that enables significantly better overall suppression of the noise compared to the respective linear filter, especially when the noise contains components of technogenic origin. Adaptive configurations of NDLs are similarly controlled by a single parameter, and are suitable for improving quality of non-stationary signals under time-varying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems, and to be used as an enhancement, or as a low-cost alternative, to the state-of-art interference mitigation methods.

Research paper thumbnail of Weighted-density approximation for general nonuniform fluid mixtures

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

In order to construct a general density-functional theory for nonuniform fluid mixtures, we propo... more In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)]. This extension corrects a deficiency in a similar extension proposed earlier by Denton and Ashcroft [Phys. Rev. A 42, 7312 (1990)], in that that functional cannot be applied to the multicomponent nonuniform fluid systems with spatially varying composition, such as solid-fluid interfaces. As a test of the accuracy of our functional, we apply it to the calculation of the freezing phase diagram of a binary hard-sphere fluid, and compare the results to simulation and the Denton-Ashcroft extension.

Research paper thumbnail of Simulation of the binary hard-sphere crystal/melt interface

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1996

Simulation of the binary hard-sphere crystal/melt interface. Ruslan L. Davidchack and Brian B. La... more Simulation of the binary hard-sphere crystal/melt interface. Ruslan L. Davidchack and Brian B. Laird Department of Chemistry, University of Kansas, Lawrence, Kansas 66045. Received 5 June 1996 We report results of molecular ...

Research paper thumbnail of Numerical Mathematics and Advanced Applications - ENUMATH 2013

Lecture Notes in Computational Science and Engineering, 2015

... 381 A Multiresolution Method for the Simulation of Sedimentation-Consolidation Processes Raim... more ... 381 A Multiresolution Method for the Simulation of Sedimentation-Consolidation Processes Raimund Burger, Alice Kozakevicius ... Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method Daniele Boffi, Lucia Gastaldi, Luca ...

Research paper thumbnail of Adaptive approximation of feedback rank filters for continuous signals

Signal Processing, 2004

Rank-based nonlinear ÿltering techniques are steadily gaining in popularity due to their robustne... more Rank-based nonlinear ÿltering techniques are steadily gaining in popularity due to their robustness. However, the analog implementation of these techniques meets with considerable conceptual and practical di culties. Here we describe an adaptive approximation for a rank ÿlter of a continuous signal expressed in terms of a system of di erential equations easily implementable in an analog circuit. The design is based on consideration of the ÿnite precision of physical measurements, which leads to simple and e cient implementation of many traditionally digital analysis tools. We also illustrate the performance of the adaptive approximation ÿlter in comparison with the respective 'exact' rank ÿlter in a boxcar moving window.

Research paper thumbnail of Efficient Detection of Periodic Orbits in Chaotic Systems by Stabilizing Transformations

SIAM Journal on Scientific Computing, 2006

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-... more An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp. 4733-4736] with a modified semi-implicit Euler iterative scheme and seeding with periodic orbits of neighbouring periods, has been shown to be highly efficient when applied to low-dimensional systems. The difficulty in applying the algorithm to higher-dimensional systems is mainly due to the fact that the number of the stabilising transformations grows extremely fast with increasing system dimension. Here we analyse the properties of stabilising transformations and propose an alternative approach for constructing a smaller set of transformations. The performance of the new approach is illustrated on the four-dimensional kicked double rotor map and the six-dimensional system of three coupled Hénon maps.

Research paper thumbnail of Signal analysis through analog representation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003

We present an approach to the analysis of signals based on analog representation of measurements.... more We present an approach to the analysis of signals based on analog representation of measurements. Methodologically, it relies on the consideration and full use of the continuous nature of a realistic, as opposed to an idealized, measuring process. Mathematically, it is based on the transformation of discrete or continuous signals into normalized continuous scalar fields with the mathematical properties of distribution functions. This approach allows a simple and efficient implementation of many traditionally digital analysis tools, including nonlinear filtering techniques based on order statistics. It also enables the introduction of a large variety of new characteristics of both one- and multi-dimensional signals, which have no digital counterparts.