We present an experimental study on the statistical properties of the injected power needed to ma... more We present an experimental study on the statistical properties of the injected power needed to maintain an inelastic ball bouncing constantly on a randomly accelerating piston in the presence of gravity. We compute the injected power at each collision of the ball with the moving piston by measuring the velocity of the piston and the force exerted on the piston by the ball. The probability density function of the injected power has its most probable value close to zero and displays two asymmetric exponential tails, depending on the restitution coefficient, the piston acceleration, and its frequency content. This distribution can be deduced from a simple model assuming quasi-Gaussian statistics for the force and velocity of the piston.
We present an experimental and theoretical study on the gravity-wave instability developing in a ... more We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor-Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gravity-wave state develops, with an m = 1 azimuthal wave number. The bifurcation is discontinuous and presents hysteresis. In contrast to previously reported work (Mujica N and Lathrop D 2006 J. Fluid Mech. 51 49-62), here we compare our experimental results with a universal model based on a quintic subcritical amplitude equation with additive noise. In general, the model describes correctly the mean free-surface oscillation amplitude and its fluctuations, although differences exist in the bistability region width and the free-surface fluctuations in the gravity wave state. These differences are due to the finite time measurements and non-linear effects, respectively. Indeed, we show that longer measurement times allow the system to transit in either direction (from or to the base state), which results in the shrinking of the bistability region. For very long measurement times, and in a very narrow range of rotation rates, the system presents a series of random reversals between both states. Finally, by removing the mean wave and flow oscillations in the measured free-surface and bulk pressure signals, we demonstrate that their dynamic fluctuations depend on the system state.
Europuim (Eu) doped aluminum oxide (Al 2 O 3 ) thin films were deposited on silicon and quartz su... more Europuim (Eu) doped aluminum oxide (Al 2 O 3 ) thin films were deposited on silicon and quartz substrates by spray pyrolysis technique, from a solution at 0.062 molar containing aluminum and europuim acetilacetonates. Eu-doping was obtained by adding to the solution the acetilacetonate in different concentrations. Structural, optical and morphological characteristics of the films, as a function of deposition conditions such as variation of the impurity concentration and deposition temperature are presented. In particular in relation to the optical characteristics (photoluminescence) of the films, it has been observed a characteristic emission associated with radiative transitions between the europium electronic energy levels. The overall spectra observed consist on several peaks associated with such transitions showing a red light emission. Structural characterization was performed by measurements of X-Ray diffraction patterns and morphological characterization by atomic force microscopy.
The diploid number of the domestic dog (Canis familiaris L) is composed of 78 chromosomes, all of... more The diploid number of the domestic dog (Canis familiaris L) is composed of 78 chromosomes, all of them morphologically acrocentric with the exception of the X chromosome which is submetacentric and the metacentric Y chromosome.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2014
One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and... more One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and complex spatiotemporal dynamics, which is characterized by the perpetual emergence of spatiotemporal dislocation chains. Using a universal amplitude equation of drifting patterns, we show that this behavior is a result of a combination of a phase instability and an advection process caused by an inhomogeneous drift force. The emergence of spatiotemporal dislocation chains is verified in numerical simulations on an optical feedback system with a non-uniform intensity pump. Experimentally this phenomenon is also observed in a tilted quasi-one-dimensional fluidized shallow granular bed mechanically driven by a harmonic vertical vibration. V C 2014 AIP Publishing LLC.
IEEE Symposium Conference Record Nuclear Science 2004., 2004
ABSTRACT 123I is a commonly used radioisotope employed in neurotransmitter SPECT studies. In addi... more ABSTRACT 123I is a commonly used radioisotope employed in neurotransmitter SPECT studies. In addition to an intense line at 159 keV, the decay scheme of this radioisotope includes a low yield (∼3%) of higher energy photons which have a non-negligible contribution to the final image when low-energy high-resolution (LEHR) collimators are used. This contribution of high-energy photons may achieve ∼28% of the total counts in the projections. The aim of this work is to model each energy component of the high-energy Point Spread Function (hPSF) for fan-beam LEHR collimators in order to develop faster Monte Carlo (MC) simulations of high-energy ray contamination. The modelling of hPSF was based on the results of simulating photons through the collimator-detector system using the MC code PENELOPE. Since low-energy PSFs models for fan-beam collimators must tend to a Gaussian distribution, we use the same function for the hPSF modelling for high-energy photons. The parameters of these Gaussian functions were obtained by minimizing the root mean square (RMS) error between each simulated hPSF and the function g(x,y) using the efficiency of the simulated hPSFs as a constraint The RMS attained with fit of g(x,y) to the simulated hPSFs was always smaller than ∼2% of the mean efficiency per pixel of the image. A very strong dependence of the efficiency on the type and thickness of the backscatter material behind the crystal was found. The hPSFs were parameterized for a wide range of energies, ranging from 350 keV to 538 keV. Our results indicate that Gaussian distributions approximate in a suitable way the hPSF responses for fan-beam collimators. This model will be an important tool to accelerate MC simulations of radiolabelled compounds which emit medium- or high-energy rays.
We report that the power driving gravity and capillary wave turbulence in a statistically station... more We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin type model. PACS numbers: 47.35.+i, 92.10.Hm, 47.20.Ky, 68.03.Cd When a dissipative system is driven in a statistically stationary regime by an external forcing, a given amount of power per unit mass, ǫ, is transfered from the driving device to the system and is ultimately dissipated. In fully developed turbulence, a flow is driven at large scales and nonlinear interactions transfer kinetic energy toward small scales where viscous dissipation takes place. In the intermediate range of scales (the inertial range) the key role of the energy flux ǫ has been first understood by Kolmogorov [1]. Using dimensional arguments, he derived the law E(k) ∝ ǫ 2/3 k −5/3 for the energy density E(k) as a function of the wavenumber k. Kolmogorov type spectra have been derived analytically in wave turbulence, i.e. in various systems involving an ensemble of weakly interacting nonlinear waves (see for instance [2] for a review). In all cases, it has been assumed that ǫ is a given constant parameter. However, it should be kept in mind that ǫ is not an input parameter in most experiments or simulations of dissipative systems. Its value is not externally controlled but determined by the impedance of the system. In addition, as we have already shown for a variety of different dissipative systems , the energy flux or related global quantities, strongly fluctuate in time although being averaged in space on the whole system or on its boundaries. These fluctuations should not be confused with small scale intermittency which occurs in fully developed turbulence. The later is related to the spotness of dissipation in space [6] and its description does not involve a time dependent ǫ.
The effect of noise in a motionless front between a periodic spatial state and an homogeneous one... more The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the front's core is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of front core is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations. 64.75.+g The description of macroscopic matter, i.e. matter composed by a large number of microscopic constituents, is usually done using a small number of coarse-grained or macroscopic variables. When spatial inhomogeneities are considered these variables are spatio-temporal fields whose evolution is determined by deterministic partial differential equations (PDE). This reduction is possible due to a separation of time scales, which allows a description in terms of the slowly varying macroscopic variables, which are in fact fluctuating variables due to the elimination of a large number of fast variables whose effect can be modelized including suitable stochastic terms (noise) in the PDE. The influence of noise in nonlinear systems has been the subject of intense experimental and theoretical investigations . Far from being merely a perturbation to the idealized deterministic evolution or an undesirable source of randomness and disorganization, noise can induce specific and even counterintuitive dynamical behavior. The most well-know examples in zero dimensional systems are noise induced transition [1] and stochastic resonance [2]. More recently, examples in spatial extended system are noise induced phase transition [3], noise-induced patterns [4-6], stochastic spatiotemporal intermittency [7] and noise-induced travelling waves [8].
We report theoretical and experimental results on 4-wave capillary wave turbulence. A system cons... more We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two inmiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair (η, Ψ). When given the symmetry z → −z, the set of weakly non-linear interacting waves display a Kolmogorov-Zakharov (KZ) spectrum n k ∼ k −4 in wave vector space. The wave system was studied experimentally with two inmiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low frequency random forcing. The power spectral density (PSD) and probability density function (PDF) of the local wave amplitude are studied. Both theoretical and experimental results are in fairly good agreement with each other.
We analyze stationary fronts connecting uniform and periodic states emerging from a patternformin... more We analyze stationary fronts connecting uniform and periodic states emerging from a patternforming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.
We present an unifying description close to a spatial bifurcation of localized states, appearing ... more We present an unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks. During the last years emerging localized structures in dissipative systems have been observed in different fields, such as domains in magnetic materials [1], chiral bubbles in liquid crystals [2], current filaments in gas discharge experiments [3], spots in chemical reactions [4], localized 2D states in fluid surface waves [5], oscillons in granular media [6], isolated states in thermal convection [7], solitary waves in nonlinear optics [8], just to mention a few.
We report on the experimental observation of spatially modulated kinks in a shallow one-dimension... more We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.
The stationary to drifting transition of a subharmonic wave pattern is studied in the presence of... more The stationary to drifting transition of a subharmonic wave pattern is studied in the presence of inhomogeneities and drift forces as the pattern wavelength is comparable with the system size. We consider a pinning-depinning transition of stationary subharmonic waves in a tilted quasi-one-dimensional fluidized shallow granular bed driven by a periodic air flow in a small cell. The transition is mediated by the competition of the inherent periodicity of the subharmonic pattern, the asymmetry of the system, and the finite size of the cell. Measurements of the mean phase velocity of the subharmonic pattern are in good agreement with those inferred from an amplitude equation, which takes into account asymmetry and finite-size effects of the system, emphasizing the main ingredients and mechanism of the transition.
We present an experimental study on the statistical properties of the injected power needed to ma... more We present an experimental study on the statistical properties of the injected power needed to maintain an inelastic ball bouncing constantly on a randomly accelerating piston in the presence of gravity. We compute the injected power at each collision of the ball with the moving piston by measuring the velocity of the piston and the force exerted on the piston by the ball. The probability density function of the injected power has its most probable value close to zero and displays two asymmetric exponential tails, depending on the restitution coefficient, the piston acceleration, and its frequency content. This distribution can be deduced from a simple model assuming quasi-Gaussian statistics for the force and velocity of the piston.
We present an experimental and theoretical study on the gravity-wave instability developing in a ... more We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor-Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gravity-wave state develops, with an m = 1 azimuthal wave number. The bifurcation is discontinuous and presents hysteresis. In contrast to previously reported work (Mujica N and Lathrop D 2006 J. Fluid Mech. 51 49-62), here we compare our experimental results with a universal model based on a quintic subcritical amplitude equation with additive noise. In general, the model describes correctly the mean free-surface oscillation amplitude and its fluctuations, although differences exist in the bistability region width and the free-surface fluctuations in the gravity wave state. These differences are due to the finite time measurements and non-linear effects, respectively. Indeed, we show that longer measurement times allow the system to transit in either direction (from or to the base state), which results in the shrinking of the bistability region. For very long measurement times, and in a very narrow range of rotation rates, the system presents a series of random reversals between both states. Finally, by removing the mean wave and flow oscillations in the measured free-surface and bulk pressure signals, we demonstrate that their dynamic fluctuations depend on the system state.
Europuim (Eu) doped aluminum oxide (Al 2 O 3 ) thin films were deposited on silicon and quartz su... more Europuim (Eu) doped aluminum oxide (Al 2 O 3 ) thin films were deposited on silicon and quartz substrates by spray pyrolysis technique, from a solution at 0.062 molar containing aluminum and europuim acetilacetonates. Eu-doping was obtained by adding to the solution the acetilacetonate in different concentrations. Structural, optical and morphological characteristics of the films, as a function of deposition conditions such as variation of the impurity concentration and deposition temperature are presented. In particular in relation to the optical characteristics (photoluminescence) of the films, it has been observed a characteristic emission associated with radiative transitions between the europium electronic energy levels. The overall spectra observed consist on several peaks associated with such transitions showing a red light emission. Structural characterization was performed by measurements of X-Ray diffraction patterns and morphological characterization by atomic force microscopy.
The diploid number of the domestic dog (Canis familiaris L) is composed of 78 chromosomes, all of... more The diploid number of the domestic dog (Canis familiaris L) is composed of 78 chromosomes, all of them morphologically acrocentric with the exception of the X chromosome which is submetacentric and the metacentric Y chromosome.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2014
One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and... more One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and complex spatiotemporal dynamics, which is characterized by the perpetual emergence of spatiotemporal dislocation chains. Using a universal amplitude equation of drifting patterns, we show that this behavior is a result of a combination of a phase instability and an advection process caused by an inhomogeneous drift force. The emergence of spatiotemporal dislocation chains is verified in numerical simulations on an optical feedback system with a non-uniform intensity pump. Experimentally this phenomenon is also observed in a tilted quasi-one-dimensional fluidized shallow granular bed mechanically driven by a harmonic vertical vibration. V C 2014 AIP Publishing LLC.
IEEE Symposium Conference Record Nuclear Science 2004., 2004
ABSTRACT 123I is a commonly used radioisotope employed in neurotransmitter SPECT studies. In addi... more ABSTRACT 123I is a commonly used radioisotope employed in neurotransmitter SPECT studies. In addition to an intense line at 159 keV, the decay scheme of this radioisotope includes a low yield (∼3%) of higher energy photons which have a non-negligible contribution to the final image when low-energy high-resolution (LEHR) collimators are used. This contribution of high-energy photons may achieve ∼28% of the total counts in the projections. The aim of this work is to model each energy component of the high-energy Point Spread Function (hPSF) for fan-beam LEHR collimators in order to develop faster Monte Carlo (MC) simulations of high-energy ray contamination. The modelling of hPSF was based on the results of simulating photons through the collimator-detector system using the MC code PENELOPE. Since low-energy PSFs models for fan-beam collimators must tend to a Gaussian distribution, we use the same function for the hPSF modelling for high-energy photons. The parameters of these Gaussian functions were obtained by minimizing the root mean square (RMS) error between each simulated hPSF and the function g(x,y) using the efficiency of the simulated hPSFs as a constraint The RMS attained with fit of g(x,y) to the simulated hPSFs was always smaller than ∼2% of the mean efficiency per pixel of the image. A very strong dependence of the efficiency on the type and thickness of the backscatter material behind the crystal was found. The hPSFs were parameterized for a wide range of energies, ranging from 350 keV to 538 keV. Our results indicate that Gaussian distributions approximate in a suitable way the hPSF responses for fan-beam collimators. This model will be an important tool to accelerate MC simulations of radiolabelled compounds which emit medium- or high-energy rays.
We report that the power driving gravity and capillary wave turbulence in a statistically station... more We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin type model. PACS numbers: 47.35.+i, 92.10.Hm, 47.20.Ky, 68.03.Cd When a dissipative system is driven in a statistically stationary regime by an external forcing, a given amount of power per unit mass, ǫ, is transfered from the driving device to the system and is ultimately dissipated. In fully developed turbulence, a flow is driven at large scales and nonlinear interactions transfer kinetic energy toward small scales where viscous dissipation takes place. In the intermediate range of scales (the inertial range) the key role of the energy flux ǫ has been first understood by Kolmogorov [1]. Using dimensional arguments, he derived the law E(k) ∝ ǫ 2/3 k −5/3 for the energy density E(k) as a function of the wavenumber k. Kolmogorov type spectra have been derived analytically in wave turbulence, i.e. in various systems involving an ensemble of weakly interacting nonlinear waves (see for instance [2] for a review). In all cases, it has been assumed that ǫ is a given constant parameter. However, it should be kept in mind that ǫ is not an input parameter in most experiments or simulations of dissipative systems. Its value is not externally controlled but determined by the impedance of the system. In addition, as we have already shown for a variety of different dissipative systems , the energy flux or related global quantities, strongly fluctuate in time although being averaged in space on the whole system or on its boundaries. These fluctuations should not be confused with small scale intermittency which occurs in fully developed turbulence. The later is related to the spotness of dissipation in space [6] and its description does not involve a time dependent ǫ.
The effect of noise in a motionless front between a periodic spatial state and an homogeneous one... more The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the front's core is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of front core is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations. 64.75.+g The description of macroscopic matter, i.e. matter composed by a large number of microscopic constituents, is usually done using a small number of coarse-grained or macroscopic variables. When spatial inhomogeneities are considered these variables are spatio-temporal fields whose evolution is determined by deterministic partial differential equations (PDE). This reduction is possible due to a separation of time scales, which allows a description in terms of the slowly varying macroscopic variables, which are in fact fluctuating variables due to the elimination of a large number of fast variables whose effect can be modelized including suitable stochastic terms (noise) in the PDE. The influence of noise in nonlinear systems has been the subject of intense experimental and theoretical investigations . Far from being merely a perturbation to the idealized deterministic evolution or an undesirable source of randomness and disorganization, noise can induce specific and even counterintuitive dynamical behavior. The most well-know examples in zero dimensional systems are noise induced transition [1] and stochastic resonance [2]. More recently, examples in spatial extended system are noise induced phase transition [3], noise-induced patterns [4-6], stochastic spatiotemporal intermittency [7] and noise-induced travelling waves [8].
We report theoretical and experimental results on 4-wave capillary wave turbulence. A system cons... more We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two inmiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair (η, Ψ). When given the symmetry z → −z, the set of weakly non-linear interacting waves display a Kolmogorov-Zakharov (KZ) spectrum n k ∼ k −4 in wave vector space. The wave system was studied experimentally with two inmiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low frequency random forcing. The power spectral density (PSD) and probability density function (PDF) of the local wave amplitude are studied. Both theoretical and experimental results are in fairly good agreement with each other.
We analyze stationary fronts connecting uniform and periodic states emerging from a patternformin... more We analyze stationary fronts connecting uniform and periodic states emerging from a patternforming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.
We present an unifying description close to a spatial bifurcation of localized states, appearing ... more We present an unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks. During the last years emerging localized structures in dissipative systems have been observed in different fields, such as domains in magnetic materials [1], chiral bubbles in liquid crystals [2], current filaments in gas discharge experiments [3], spots in chemical reactions [4], localized 2D states in fluid surface waves [5], oscillons in granular media [6], isolated states in thermal convection [7], solitary waves in nonlinear optics [8], just to mention a few.
We report on the experimental observation of spatially modulated kinks in a shallow one-dimension... more We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.
The stationary to drifting transition of a subharmonic wave pattern is studied in the presence of... more The stationary to drifting transition of a subharmonic wave pattern is studied in the presence of inhomogeneities and drift forces as the pattern wavelength is comparable with the system size. We consider a pinning-depinning transition of stationary subharmonic waves in a tilted quasi-one-dimensional fluidized shallow granular bed driven by a periodic air flow in a small cell. The transition is mediated by the competition of the inherent periodicity of the subharmonic pattern, the asymmetry of the system, and the finite size of the cell. Measurements of the mean phase velocity of the subharmonic pattern are in good agreement with those inferred from an amplitude equation, which takes into account asymmetry and finite-size effects of the system, emphasizing the main ingredients and mechanism of the transition.
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Papers by Claudio Falcon