Noiseless System Research Articles

Large deviations for small noise diffusions over long time

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers (LLN) of the empirical measure in this asymptotic regime is given by the unique equilibrium of the noiseless dynamics. Due to degeneracy of the noise in the limit, the methods of Donsker and Varadhan [Comm. Pure Appl. Math. 29 (1976), pp. 389–461] are not directly applicable and new ideas are needed. Second, we study a system of slow-fast diffusions where both the slow and the fast components have vanishing noise on their natural time scales. This time the LLN is governed by a degenerate averaging principle in which local equilibria of the noiseless system obtained from the fast dynamics describe the asymptotic evolution of the slow component. We establish a large deviation principle that describes probabilities of divergence from this behavior. On the one hand our methods require stronger assumptions than the nondegenerate settings, while on the other hand the rate functions take simple and explicit forms that have striking differences from their nondegenerate counterparts.

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

Bias-Correction Errors-in-Variables Hammerstein Model Identification

In this paper, a Bias-Correction Least-Squares (BCLS) algorithm is proposed for identifying block-oriented Errors-In-Variables nonlinear Hammerstein (EIV-Hammerstein) systems. Due to both the input and output of the EIV-Hammerstein system are observed with additive white noises, the estimation bias of traditional LS algorithm is introduced. The estimation bias is derived from a consistency point of view, which is a function about noises variances and monomial of noiseless system input-output measurements. A bias-estimation scheme based only on the available noisy measurements is then proposed for consistent identification of the monomial of noiseless system input-output measurements in a recursive form. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the unknown noise variances for practical applications. Such that the noise effect can be eliminated and the consistent estimated parameters are obtained. The effectiveness of the proposed method is demonstrated by a simulation example and an experimental prototype of wireless power transfer system.

Two paradigmatic scenarios for inverse stochastic resonance.

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated with a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow-fast analysis of the corresponding noiseless systems.

Phase-space diffusion of charged particles induced by random fluctuations of relative gyrophases in the presence of finite amplitude circularly polarized electromagnetic waves

A stochastic model to describe the phase-space diffusion of charged particles induced by random fluctuations of relative gyrophases in the presence of parallel propagating, circularly polarized electromagnetic waves is discussed. The perturbation analysis around the equilibrium points of the noiseless system shows the coexistence of classical diffusion and trapping oscillation. Even if the equation of motions for pitch angle does not include noise terms, the pitch angle diffusion occurs due to the noise term in the equation of the relative gyrophase and the existence of the finite amplitude wave. The resultant theory is validated by using numerical results of test particle simulations; when distributions of the relative gyrophases and pitch angle cosines are close to Gaussian, the classical diffusion and trapping oscillation are observed. With increasing wave amplitude and/or the strength of noise, the pitch angle diffusion becomes subdiffusive.

Numerical Research on the Vortex Center on the Forward-Swept 3-D Wind Turbine Blades at Low Rotational Speed

This paper studies the CFD simulation of forward three-dimensional (3-D) horizontal axis wind turbine (HAWT) blades. Using logarithmic grid and Q-criterion to learn the vortex dynamics around the blades at low rotational speed. The computational fluid dynamics (CFD) simulation uses Q-criterion to probe vortices and logarithmic grid to emphasize the micro-gridding effect of the turbulent boundary layer. The visualization & measurement of the simulation results give the coefficient of pressure (Cp). For forward 3-D wind turbine blade, at low rotational speed, the strongly accelerated laminar region surrounds the lower blade, and the decelerated tip blade region coalesce each other give rise to a reverse limiting streamline, eroding the laminar region further until a little is left on the tip of the blade. The "reverse limiting streamline" grows inward radially, the area is narrowing closing to the leading edge of the blade tip. The second side of the rolled-up vortex appears the velocity ratio (Uc/Ulocal) of the second vortices are higher than the main vortex cores. For radius R=1.547 m, U=12 m/s, at 210 RPM, CL and CD values reach a maximum with fully laminar tip conditions. While at 120 RPM, the CL and CD values reach a minimum in the absence of laminar tips. The results show the detailed vortex dynamic pattern surround the blades, give more understanding to design laminar 3-D blade toward a noiseless wind turbine system.

Development of a new micro CHP pellet stove technology

BIOS and RIKA developed within the ERA-NET-project “Small-scale BM based CHP” a new micro CHP technology based on a wood pellet stove (thermal capacity 10.5 kW) with a thermoelectric generator (TEG), that enables the operation of the stove without electric grid connection. Thereby, the wear- and maintenance-free and also noiseless TEG system is cooled by a water circuit which makes it possible to supply an additional room with heat. To achieve a self-sustaining operation of the pellet stove a TEG with an electric power of up to 50 W was installed into the casing of the pellet stove and the electricity consumption has been reduced significantly by an optimization of the control system and the selection of appropriate low voltage components. Based on transient system calculations and CFD simulations as well as test runs with two testing plants the system has been optimized. To demonstrate the practical suitability of the new technology in real life, 8 h load cycle tests were carried out. At these tests overall efficiencies up to 92.6% were achieved and in addition to the coverage of the own electricity consumption of the stove, 50 W h surplus electricity were produced which can be used to charge mobile phones or other small consumers.

Small noise and long time phase diffusion in stochastic limit cycle oscillators

We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise – that is, we modulate the noise by a factor ε↘0 – and on a long time horizon. We prove explicit estimates on the proximity of the noisy trajectory and the limit cycle up to times exp⁡(cε−2), c>0, and we show both that on the time scale ε−2 the dephasing (i.e., the difference between noiseless and noisy system measured in a natural coordinate system that involves a phase) is close to a Brownian motion with constant drift, and that on longer time scales the dephasing dynamics is dominated by the drift. The natural choice of coordinates, that reduces the dynamics in a neighborhood of the cycle to a rotation, plays a central role and makes the connection with the applied science literature in which noisy limit cycle dynamics are often reduced to a diffusion model for the phase of the limit cycle.

Nonadaptive Group Testing Based on Sparse Pooling Graphs

An information theoretical analysis of nonadaptive group testing schemes based on sparse pooling graphs is presented. A pooling graph is a bipartite graph for which the adjacency matrix is a pooling matrix. The binary status of the objects to be tested are modeled by independent identically distributed. Bernoulli random variables with probability $p$ . An $(l, r, n)$ -regular pooling graph is a bipartite graph in which the left nodes have degree $l$ , the right nodes have degree $r$ , and $n$ is the number of left nodes. The main contribution of this paper is a direct coding theorem that gives the conditions for the existence of an estimator that can achieve an arbitrarily small probability of error. An estimator is a function that uses observations to infer the state of an object. The direct coding theorem is proved by averaging the upper bound on the probability of the estimation error of the typical set estimator over an $(l, r, n)$ -regular pooling graph ensemble. Numerical results indicate sharp threshold behaviors in the asymptotic regime. These results can provide a concrete benchmark for nonadaptive group testing of existing and emerging detection algorithms over a noiseless system.

Secure State Estimation Against Sensor Attacks in the Presence of Noise

We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on the achievable state estimation error given an upper bound on the number of attacked sensors. The proposed state estimator involves Kalman filters operating over subsets of sensors to search for a sensor subset which is reliable for state estimation. To further improve the subset search time, we propose Satisfiability Modulo Theory based techniques to exploit the combinatorial nature of searching over sensor subsets. Finally, as a result of independent interest, we give a coding theoretic view of attack detection and state estimation against sensor attacks in a noiseless dynamical system.

The Control of The Lorenz Chaotic System Blended With The Noise

In this study, the Lorenz chaotic system behavior is investigated according to the change in the noise of the system and measurement. The noise was emerged as an important impact on the Lorenz chaotic system. The discrete-time LQR ( Linear Quadratic Regulator) control method and discrete-time PI controller method have been used to the noisy system controls. Noise was accepted as a destructor that changes the output behavior of the chaotic system. Noisy system outputs were enforced to move to the equilibrium points by the support of controllers. Optimization of the controller parameters for noiseless system models was performed using a genetic algorithm method. Then, both control system algorithms determined as successful in transporting to the equilibrium point for state variables which are blended with the noise. Changes, associated with the noise conditions are given in the graphics and tables. Besides, the error performance criteria and the control performance criteria were obtained to evaluate the results. This study was performed by MATLAB-Simulink simulation program.

Noise-induced transitions in optomechanical synchronization

We study how quantum and thermal noise affects synchronization of two optomechanical limit-cycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either in-phase or anti-phase. Taking into account the fundamental quantum noise, we find a regime where fluctuations drive transitions between these classical synchronization states. We investigate how this ‘mixed’ synchronization regime emerges from the noiseless system by studying the classical-to-quantum crossover and we show how the time scales of the transitions vary with the effective noise strength. In addition, we compare the effects of thermal noise to the effects of quantum noise.

A Novel Biometric System based on Hybrid Fusion Speech, Signature and Tongue

There is urgent need to make behavioural biometric systems more reliable, robust and accurate. This paper presents feature level fusion of offline signature and speech and tongue biometrics. The fusion of speech and signature with tongue made the system more efficient. MFCC is used for feature extraction in speech and in signature DCT is used which is widely used for image and texture feature extraction. While the features of tongue are extracted using SIFT algorithm. Hybrid weighted average using Apirori two item set is applied for the fusion of extracted features of all the modalities. SVC2004 signature database are used for experimental results. Tongue database was collected by capturing pictures using digital camera while for speech CMU_ARCTIC database which is available at Language Technologies Institute at Carnegie Mellon University is used in the work. Features for both noisy and non-noisy samples have been collected separately. Gaussian noise was added to the system to check the performance in noisy environment. The proposed system also works efficiently on filtered noisy modalities with accuracy of 80%. The accuracy of the noiseless system is 88.75% with 0.06 % of FAR and with 0.05% of FRR and the noisy system have FAR 0.05% and FRR 0.15%. The ROC curves are calculated.

A compact and portable X-ray beam position monitor using Medipix3

The present work reports on the design and implementation of a novel portable X-ray beam diagnostics (XBPM) device. The device is transparent to the X-ray beam and provides real-time measurements of beam position, intensity, and size. The measurement principle is based on a pinhole camera which records scattered radiation from a Kapton foil which is placed in the beam path. The use of hybrid detectors (Medipix3) that feature a virtually noiseless readout system with capability of single photon detection and energy resolving power enables the diagnostics with a better resolution and higher sensitivity compared to the use of traditional indirect X-ray detection schemes. We describe the detailed system design, which consists of a vacuum compatible focal plane sensor array, a sensor conditioning and readout board and a heterogeneous data processing unit, which also acts as a network server that handles network communications with clients. The readout protocol for the Medipix3 sensor is implemented using field programmable gate array (FPGA) logic resulting in a versatile and scalable system that is capable of performing advanced functions such as data compression techniques and feature extraction. For the system performance measurements, we equipped the instrument with a single Medipix3 die, bump bonded to a Si sensor, rather than four for which it was designed. Without data compression, it is capable of acquiring magnified images and profiles of synchrotron X-ray beams at a transfer rate through Ethernet of 27 frames/s for one Medipix3 die.

Noise effect on statistical properties of type-I intermittency

In this work we analyze the noise effect on type-I intermittency, for which we develop a methodology based on a recently proposed technique used to model the reinjection probability density (RPD). This new methodology allows us to study the noise effect on the intermittency statistical properties for relatively large noise strengths in a quadratic map with different reinjection mechanisms. We show that this procedure allows to predict the behavior of the noisy and noiseless system using the results of the M(x) function which is implemented to obtain the RPD function. We also derive an analytical approximation for the probability density of the laminar lengths and we obtain results for the average laminar length. All analytical approaches show a good agreement with the numerical results even though the statistical properties are calculated using either the noisy or noiseless data, however in some cases the description of the noiseless system using the noisy data can be inaccurate. In addition, we show that occasionally the presence of noise could be not detected due to the results behave as they would be corresponding to a noiseless system. This aspect may have important consequences especially when working with experimental data.

Spectra of delay-coupled heterogeneous noisy nonlinear oscillators

Nonlinear oscillators that are subject to noise and delayed interaction have been used to describe a number of dynamical phenomena in Physics and beyond. Here we study the spectral statistics (power and cross-spectral densities) of a small number of noisy nonlinear oscillators and derive analytical approximations for these spectra. In our paper, individual oscillators are described by the normal form of a supercritical or subcritical Hopf bifurcation supplemented by Gaussian white noise. Oscillators can be distinguished from each other by their frequency, bifurcation parameter, and noise intensity. Extending previous results from the literature, we first calculate in linear response theory the power spectral density and response function of the single oscillator in both super- and subcritical parameter regime and test them against numerical simulations. For small heterogeneous groups of oscillators (N = 2 or 3), which are coupled by a delayed linear term, we use a linear response ansatz to derive approximations for the power and cross-spectral densities of the oscillators within this small network. These approximations are confirmed by comparison with extensive numerical simulations. Using the theory we relate the peaks in the spectra of the homogeneous system (identical oscillators) to periodic solutions of the deterministic (noiseless) system. For two delay-coupled subcritical Hopf oscillators, we show that the coupling can enhance the coherence resonance effect, which is known to occur for the single subcritical oscillator. In the case of heterogeneous oscillators, we find that the delay-induced characteristic profile of the spectra is conserved for moderate frequency detuning.

Self-Convectional Three-Dimensional Integrated Circuit Cooling System using Micro Flat Heat Pipe for Portable Devices

A self-convectional three-dimensional integrated circuit (3D IC) cooling system using micro flat heat pipes (MFHP) was proposed and the electrothermal behavior of the proposed structure was modeled by an equivalent circuit for simulation. Experimental measurements using the fabricated evaluation board for the 3D IC cooling system demonstrated that the temperature of the chip under test drops about 42°C due to the MFHP on the chip in steady state. The cooling performance of the proposed system is satisfactory for use as a 3D IC cooling system for mobile applications. We have applied the proposed system to the central processing unit cooler of a commercial laptop personal computer (PC). The volume of an air cooling system with conventional heat pipes for a laptop PC is about 40 times larger than that of the proposed system. However, the cooling performance of the proposed system is comparable to the original air cooler in the laptop PC both for horizontal and for vertical operation of the MFHP. The main advantage of the proposed cooler is that it is a slim, noiseless system that operates without additional cooling power consumption. The experimental results for vertical and horizontal operation of the MFHP demonstrate the possibility of the proposed self-convection MFHP architecture as a solution for the cooling system of 3D ICs that is suitable for portable devices.

Weak-noise limit of a piecewise-smooth stochastic differential equation

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Adaptive Modulation in Networked Control Systems with Application in Smart Grids

In communication for the feedback control of a noiseless dynamical system, adaptive modulation is studied to adapt the modulation scheme to the physical system state or parameters in networked control systems. The impact of delay and packet drop rate incurred by modulation is studied. Then, the adaptive modulation is formulated as optimization problems for the scenarios in which the modulation is adaptive to either the system parameters or system state. Numerical simulations in the context of smart grids demonstrate the validity of the proposed adaptive modulation scheme.

Effect of noise on the reinjection probability density in intermittency

This paper analyzes the effect of noise in type-II and type-III intermittency, with respective local Poincaré maps of xn+1=(1+ε)xn+(1-ε)xn3 and xn+1=-(1+ε)xn-axn3 (a>0). We develop a method to obtain the noisy reinjection probability density (NRPD), which basically consists in extending a recent procedure used to derive the noiseless reinjection probability density (RPD). Our approach also provides information to accurately describe the noiseless system. We also derive the probability density of the laminar length. Our analytical results show a good agreement with numerical simulations. Finally, we have also found that, for large values of the instability parameter ε, the characteristic relations approach the associated ones to the noiseless intermittency. However, for low values of the instability parameter ε, the characteristic relations reach a saturation level that depends on the NRPD.