Narrow Results

In this communication, a familiar physical phenomenon along with a time-dependent concentration source in a one-dimensional fractional differential advection–diffusion has been worked out. The problem is supported with the boundary with initial and boundary conditions. First of all, the results for the nondimensional classical advection–diffusion process are deliberated utilizing the Laplace coupled with finite sine-Fourier transforms analytically. Later on, the analysis is expanded for different fractional operators. The inspection of memory factors is presented through Mathcad. The impacts of the fractional (memory) parameter upon the solute concentration are discussed by making use of Mathcad15. A detailed physical significance of the fractional problem in view of the parameters is studied. It is noted that the decreasing change in concentration is associated with the larger values of noninteger parameter.

The generation and the growth of vapor bubbles in metastable liquid Helium-3 are studied. The finite diffuse layer of vapor bubble, the temperature dependence of the surface tension and the relaxation processes are taken into consideration. We show that the growth of bubble in overheated liquid Helium-3 is significantly influenced by the memory effects caused by the dynamic Fermi-surface distortions. In particular, the increase of bubble is strongly hindered and accompanied by the characteristic oscillations of the bubble radius. The oscillations of the bubble radius disappear in a short relaxation-time limit where the memory effects are negligible.

There has been intensive research in memoryless nonlinear behavioral modeling of power amplifiers (PAs). But in broadband communication systems, memory effects of PAs can no longer be ignored and traditional memoryless model cannot accurately characterize the input-output relationship of PAs. In order to treat memory effects and reduce the complexity of general Volterra model, a new behavioral PA model based on modified Volterra series is proposed. Since the characteristics of power amplifiers change during transmission time, a recursive least squares algorithm with size-fixed observation matrices is developed to update the parameters of the PA model. This identification algorithm, which uses only the latest sample data to identify the parameters, can decrease computational complexity and data storage space needed for identification. Simulations are carried out to validate the performances of the proposed PA model and identification algorithm.

This paper reports a refined multi-tone waveform measurement system for the robust characterization and optimization of nonlinear microwave devices when driven by broadband multi-tone stimuli. This enhanced system has the ability to present specific, constant broadband impedances, not only at baseband (IF) frequencies, but also at RF frequencies, particularly, around the carrier and significant harmonics. This functionality is key in studying the effects of out-of-band impedance termination on both short and long-term electrical memory effects. Achieving such comprehensive impedance control across wide modulation bandwidths is also critical in allowing the "emulation" of emerging power amplifier modes and architectures, and the subsequent waveform characterization of devices operating in these complex and often dynamic impedance environments. Initially, the baseband load-pull capabilities of the enhanced measurement system are experimentally demonstrated through the measurement of adjacent channel power (ACP) behavior of a class AB biased 10 W GaN HEMT, in response to a varying baseband load. Complete baseband and RF impedance control is then demonstrated through the emulation and analysis of a modulated Class-J impedance environment, which interestingly highlights the presence of separate optimum baseband impedance conditions necessary for the suppression of individual IM products.

In this paper, the FPGA implementation of the generalized parallel two-box (GPTB) model is proposed. The blocks such as multipliers, complex magnitude calculator, and magnitude powers calculator have been utilized to implement the GPTB model. In the implementation of the proposed model, a total of 30 complex multipliers, 56 noncomplex multipliers and 56 adders were used. The GPTB DPD model has been implemented by using System Generator and Vivado software. The FPGA with a part number of xc7vx690t-3 from Xilinx has been employed to implement the model. The simulation results demonstrate the correctness of the implemented model in Vivado. Also, the verification of the GPTB model is accomplished by means of the simulation of the transmitter excited by QAM signals in the ADS software. The measure of an adjacent channel power ratio (ACPR) decreased by about 16dB as a result of the simulation.

Consider the one-dimensional wave equation on a unit interval, where the left-end boundary condition is linear, pumping energy into the system, while the right-end boundary condition is self-regulating of the van der Pol type with a cubic nonlinearity. Then for a certain parameter range it is now known that chaotic vibration occurs. However, if the right-end van der Pol boundary condition contains an extra linear displacement feedback term, then it induces a memory effect and considerable technical difficulty arises as to how to define and determine chaotic vibration of the system. In this paper, we take advantage of the extra margin property of the reflection map and utilize properties of homoclinic orbits coupled with a perturbation approach to show that for a small parameter range, chaotic vibrations occur in the sense of unbounded growth of snapshots of the gradient. The work also has significant implications to the occurrence of chaotic vibration for the wave equation on a 3D annular domain.

A general theory of non-local materials, with linear constitutive equations and memory effects, is developed within a thermodynamic framework. Several free energy and dissipation functionals are constructed and explored. These include an expression for the minimum free energy and a functional that is a free energy for important categories of memory kernels and is explicitly a functional of the minimal state. The functionals discussed have a similar general form to the corresponding expressions for simple materials. A number of new results are derived for them, most of which apply equally to both types of material. In particular, detailed formulae are given for these quantities in the case of sinusoidal histories.

In this study, we examine a modified heat equation with memory and nonlinear source. The source function is considered under two different conditions, the global Lipschitz and the exponential growth functions. For the first condition, a special weighted Banach space is applied to deduce a desired result without any assumption on sufficiently small time and initial data. For the second condition of exponential growth, we apply the Moser–Trudinger inequality to cope with the source function, and a special time-space norm to deduce the unique existence of a global solution in regard to sufficiently small data. The main objective of this work is to prove the global existence and uniqueness of mild solutions. Besides the solution techniques, our main arguments are also based on the Banach fixed point theorem and linear estimates for the mild solution. The highlight of this study is that it is the first work on the global well-posedness for the mild solution of the fractional heat conduction with memory and nonlinear sources.

We analyze the communication efficiency of quantum information transfer along unmodulated spin chains by computing the communication rates of various protocols. The effects of temporal correlations are discussed, showing that they can be exploited to boost the transmission efficiency.

It is known that entanglement dynamics of two non-interacting qubits, locally subjected to classical environments, may exhibit revivals. A simple explanation of this phenomenon may be provided by using the concept of hidden entanglement (HE), which signals the presence of entanglement that may be recovered without the help of nonlocal operations. Here we discuss the link between HE and the (non-Markovian) flow of classical information between the system and the environment.

Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics that define a stochastic process lies at the heart of any proper treatment of memory effects. This is well understood in classical theory, where a hierarchy of joint probability distributions completely characterizes the process at hand. However, attempting to generalize this notion to quantum mechanics is problematic: observing realizations of a quantum process necessarily disturbs the state of the system, breaking an implicit, and crucial, assumption in the classical setting. This issue can be overcome by separating the experimental interventions from the underlying process, enabling an unambiguous description of the process itself and accounting for all possible multi-time correlations for any choice of interrogating instruments.

In this paper, using a novel framework for the characterization of quantum stochastic processes, we first solve the long standing question of unambiguously describing the memory length of a quantum processes. This is achieved by constructing a quantum Markov order condition, which naturally generalizes its classical counterpart for the quantification of finite-length memory effects. As measurements are inherently invasive in quantum mechanics, one has no choice but to define Markov order with respect to the interrogating instruments that are used to probe the process at hand: different memory effects are exhibited depending on how one addresses the system, in contrast to the standard classical setting. We then fully characterize the structural constraints imposed on quantum processes with finite Markov order, shedding light on a variety of memory effects that can arise through various examples. Finally, we introduce an instrument-specific notion of memory strength that allows for a meaningful quantification of the temporal correlations between the history and the future of a process for a given choice of experimental intervention.

These findings are directly relevant to both characterizing and exploiting memory effects that persist for a finite duration. In particular, immediate applications range from developing efficient compression and recovery schemes for the description of quantum processes with memory to designing coherent control protocols that efficiently perform information-theoretic tasks, amongst a plethora of others.

A functional polyimide (CF3 PI) was used as the active layer in our present work for electrical resistive memory device applications. Current–voltage ($I$–$V$) characteristics analysis on the polyimide memory devices indicates that the polyimide possesses a nonvolatile rewritable flash characteristic with an ON/OFF current ratio of about 10⁴ at the threshold voltage of around $-1.2$V and 3.8V. In addition, the device using the CF3 PI as the active layer reveals excellent long-term operation stability with the endurance of reading cycles up to 10⁸ under a voltage pulse and retention times for at least 10⁶s under constant voltage stress (1V). The conduction mechanisms are elucidated on the basis of the thermionic emission theory and filament conduction.