Search

We discuss the analysis of a piezoelectric energy harvester for random mechanical vibrations, and we assess the performance improvement guaranteed by interposing a matching network between the transducer and the electrical load, in terms of average output power and power efficiency. The mathematical model describing the harvester is a system of stochastic differential equations, where both cases of linear and nonlinear devices are considered. In the linear case, the power delivered to the load is increased by a factor of about 20 with respect to the direct connection, with a similar increase in the conversion efficiency. In the nonlinear case, we use a moment closure technique to calculate the first- and second-order moments of the electro-mechanical variables in the weak noise limit. Moment calculation is used to determine the optimal values of the matching network components that maximize the performance. In the strong noise limit, the state equations are integrated numerically to determine the same performance metrics. Our analysis shows that a properly designed matching network improves the performance by a significant amount, especially at low noise intensity. [ABSTRACT FROM AUTHOR]

This paper reviews advanced modeling and analysis techniques useful in the description, design, and optimization of mechanical energy harvesting systems based on the collection of energy from vibration sources. The added value of the present contribution is to demonstrate the benefits of the exploitation of advanced techniques, most often inherited from other fields of physics and engineering, to improve the performance of such systems. The review is focused on the modeling techniques that apply to the entire energy source/mechanical oscillator/transducer/electrical load chain, describing mechanical–electrical analogies to represent the collective behavior as the cascade of equivalent electrical two-ports, introducing matching networks enhancing the energy transfer to the load, and discussing the main numerical techniques in the frequency and time domains that can be used to analyze linear and nonlinear harvesters, both in the case of deterministic and stochastic excitations. [ABSTRACT FROM AUTHOR]

It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this perspective, we discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that are scalable. DMMs can be realized with non-linear dynamical systems with memory. The latter property allows the realization of a new type of Boolean logic, one that is self-organizing. Self-organizing logic gates are “terminal-agnostic,” namely, they do not distinguish between the input and output terminals. When appropriately assembled to represent a given combinatorial/optimization problem, the corresponding self-organizing circuit converges to the equilibrium points that express the solutions of the problem at hand. In doing so, DMMs take advantage of the long-range order that develops during the transient dynamics. This collective dynamical behavior, reminiscent of a phase transition, or even the “edge of chaos,” is mediated by families of classical trajectories (instantons) that connect critical points of increasing stability in the system's phase space. The topological character of the solution search renders DMMs robust against noise and structural disorder. Since DMMs are non-quantum systems described by ordinary differential equations, not only can they be built in hardware with the available technology, they can also be simulated efficiently on modern classical computers. As an example, we will show the polynomial-time solution of the subset-sum problem for the worst cases, and point to other types of hard problems where simulations of DMMs' equations of motion on classical computers have already demonstrated substantial advantages over traditional approaches. We conclude this article by outlining further directions of study. [ABSTRACT FROM AUTHOR]

Circuit theory and nonlinear dynamics are instrumental to design efficient energy harvesters for ambient mechanical vibrations. In this work, we show that an impedance matching networks can be designed that maximizes the harvested power, and improves the power efficiency. The proposed matching network achieves impedance matching at a single frequency, that can be chosen at will by the designer, and does not need to coincide with the resonant frequency of the harvester. Moreover, the matching network also increases the harvested power over a wide frequency bandwidth. According to our numerical simulations, the matching network increases the maximum harvested power by a factor greater than 3, and the power harvested over the whole frequency spectrum by a factor of 6. The frequency bandwidth can be further extended considering nonlinear energy harvesters. Even using the matching network designed for the linear case, performance is significantly nonetheless improved for the nonlinear harvester. [ABSTRACT FROM AUTHOR]

The study of fluctuations in oscillators has been a classical research topic in mathematics, physics, and engineering since the first half of the 20th century [1]-[4]. Besides the intellectual fascination for mathematically difficult problems, the importance of the topic is deeply rooted in practical applications, mainly in the fields of RF and microwave electronics and also telecommunications. In fact, defining a precise frequency reference is fundamental for many applications, both electrical (e.g., transmitters and receivers) and optical (e.g., lasers). The broadening of the generated spectral line is mainly due to the phase-noise component of oscillator fluctuations, which consequently is the most commonly studied feature of oscillator noise (see [5] for a recent and exhaustive review). In a dual perspective, the definition of a precise time reference is also extremely important for digital applications, thus implying the necessity to keep under control the time jitter in clocked and in sampled systems. From a theoretical standpoint, phase noise and time jitter are simply two sides of the same coin, a manifestation of the oscillator?s noisy behavior. As the microwave engineer is more often interested in the phase-noise characterization, we discuss only the latter. The time-jitter estimation is discussed, for instance, in [6]. [ABSTRACT FROM AUTHOR]

We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with infinite memory, i.e., a dependence on the whole previous history. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology. [ABSTRACT FROM AUTHOR]

Optimization problems pervade essentially every scientific discipline and industry. A common form requires identifying a solution satisfying the maximum number among a set of many conflicting constraints. Often, these problems are particularly difficult to solve, requiring resources that grow exponentially with the size of the problem. Over the past decades, research has focused on developing heuristic approaches that attempt to find an approximation to the solution. However, despite numerous research efforts, in many cases even approximations to the optimal solution are hard to find, as the computational time for further refining a candidate solution also grows exponentially with input size. In this paper, we show a noncombinatorial approach to hard optimization problems that achieves an exponential speed-up and finds better approximations than the current state of the art. First, we map the optimization problem into a Boolean circuit made of specially designed, self-organizing logic gates, which can be built with (nonquantum) electronic elements with memory. The equilibrium points of the circuit represent the approximation to the problem at hand. Then, we solve its associated nonlinear ordinary differential equations numerically, towards the equilibrium points. We demonstrate this exponential gain by comparing a sequential MATLAB implementation of our solver with the winners of the 2016 Max-SAT competition on a variety of hard optimization instances. We show empirical evidence that our solver scales linearly with the size of the problem, both in time and memory, and argue that this property derives from the collective behavior of the simulated physical circuit. Our approach can be applied to other types of optimization problems, and the results presented here have far-reaching consequences in many fields. [ABSTRACT FROM AUTHOR]

It is well known that dynamical systems may be employed as computing machines. However, not all dynamical systems offer particular advantages compared to the standard paradigm of computation, in regard to efficiency and scalability. Recently, it was suggested that a new type of machines, named digital -hence scalable- memcomputing machines (DMMs), that employ non-linear dynamical systems with memory, can solve complex Boolean problems efficiently. This result was derived using functional analysis without, however, providing a clear understanding of which physical features make DMMs such an efficient computational tool. Here, we show, using recently proposed topological field theory of dynamical systems, that the solution search by DMMs is a composite instanton. This process effectively breaks the topological supersymmetry common to all dynamical systems, including DMMs. The emergent long-range order - a collective dynamical behavior- allows logic gates of the machines to correlate arbitrarily far away from each other, despite their non-quantum character. We exemplify these results with the solution of prime factorization, but the conclusions generalize to DMMs applied to any other Boolean problem. [ABSTRACT FROM AUTHOR]

We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP=P question related to constraints of poly-resources resolvability. [ABSTRACT FROM AUTHOR]

We discuss the effect of the estimation of the amplitude variations on the noise-induced frequency shift in nonlinear oscillators. The analysis is based on a general reduction approach to a phase macromodel making use of the Itô interpretation of the stochastic differential equations representing noisy autonomous systems. We show that a significant improvement of the accuracy can be obtained by using the average value of the amplitude component determined from a linearization of the amplitude equation. [ABSTRACT FROM PUBLISHER]

Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials. [ABSTRACT FROM AUTHOR]

We present a mixed time-frequency domain algorithm for the approximate computation of the Floquet quantities (exponents and both direct and adjoint eigenvectors) resulting from the linearization of index-1 differential-algebraic equations around a periodic limit cycle. The approach allows to select the number of Floquet exponents to be calculated approximating the matrix of the obtained eigenvalue problem. The error in the evaluation (for both exponents and eigenvectors) is proved to tend to zero along with the ratio between the norms of the neglected and retained rows of the relevant matrix. [ABSTRACT FROM AUTHOR]

Starting from the definition of the stochastic differential equation for amplitude and phase fluctuations of an oscillator described by an ordinary differential equation, we study the associated Fokker-Planck equation by using tools from stochastic integral calculus, harmonic analysis and Floquet theory. We provide an asymptotic characterization of the relevant correlation functions, showing that within the assumption of a linear perturbative analysis for the amplitude fluctuations phase noise and orbital fluctuations at the same time are asymptotically statistically independent, and therefore the nonlinear perturbative analysis of phase noise recently derived still exactly holds even if orbital noise is taken into account. [ABSTRACT FROM AUTHOR]

We discuss the impact of orbital fluctuations on the noise spectrum of a free-running oscillator, exploiting a rigorous nonlinear perturbative analysis based on the Floquet theory, and providing evidence of its relevance for high-Q oscillators. [ABSTRACT FROM PUBLISHER]

In this letter we present the first implementation of Floquet theory for the large-signal stability analysis of power amplifiers including transmission lines. We compare a few lumped-parameter and distributed designs of a combined class-B PA with equivalent in-band performance but different layouts. Distributed designs are shown to induce distinctive features from the stability standpoint, in particular with reference to the onset of odd-mode oscillations. These results show the potential and practical interest, also from the layout verification standpoint, of the extension of Floquet theory to the analysis of circuits including distributed elements. [ABSTRACT FROM PUBLISHER]

Recent work on quantum annealing has emphasized the role of collective behavior in solving optimization problems. By enabling transitions of clusters of variables, such solvers are able to navigate their state space and locate solutions more efficiently despite having only local connections between elements. However, collective behavior is not exclusive to quantum annealers, and classical solvers that display collective dynamics should also possess an advantage in navigating a nonconvex landscape. Here we give evidence that a benchmark derived from quantum annealing studies is solvable in polynomial time using digital memcomputing machines, which utilize a collection of dynamical components with memory to represent the structure of the underlying optimization problem. To illustrate the role of memory and clarify the structure of these solvers we propose a simple model of these machines that demonstrates the emergence of long-range order. This model, when applied to finding the ground state of the Ising frustrated-loop benchmarks, undergoes a transient phase of avalanches which can span the entire lattice and demonstrates a connection between long-range behavior and their probability of success. These results establish the advantages of computational approaches based on collective dynamics of continuous dynamical systems. [ABSTRACT FROM AUTHOR]

The article presents a study that explores about the global minimization via classical tunneling assisted by collective force field formation. It mentions the mechanism as appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.

In Traversa and Di Ventra [Chaos 27, 023107 (2017)] we argued, without proof, that if the nonlinear dynamical systems with memory describing the class of digital memcomputing machines (DMMs) have equilibrium points, then no periodic orbits can emerge. In fact, the proof of such a statement is a simple corollary of a theorem already demonstrated in Traversa and Di Ventra [Chaos 27, 023107 (2017)]. Here, we point out how to derive such a conclusion. Incidentally, the same demonstration implies absence of chaos, a result we have already demonstrated in Di Ventra and Traversa [Phys. Lett. A 381, 3255 (2017)] using topology. These results, together with those in Traversa and Di Ventra [Chaos 27, 023107 (2017)], guarantee that if the Boolean problem the DMMs are designed to solve has a solution, the system will always find it, irrespective of the initial conditions. [ABSTRACT FROM AUTHOR]