搜索结果：Nano convergence

Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper, we analyze convergence properties of the BMS algorithm by leveraging its interpretation as an optimization procedure, which is known but has been underutilized in existing convergence studies. Whereas existing results on convergence properties applicable to multi-dimensional data only cover the case where all the blurred data point sequences converge to a single point, this study provides a convergence guarantee even when those sequences can converge to multiple points, yielding multiple clusters. This study also shows that the convergence of the BMS algorithm is fast by further leveraging geometrical characterization of the convergent points.

Mutual synchronization of N serially connected spintronic nano-oscillators increases their coherence by a factor $N$ and their output power by $N^2$. Increasing the number of mutually synchronized nano-oscillators in chains is hence of great importance for better signal quality and also for emerging applications such as oscillator-based neuromorphic computing and Ising machines where larger N can tackle larger problems. Here we fabricate spin Hall nano-oscillator chains of up to 50 serially connected nano-constrictions in W/NiFe, W/CoFeB/MgO, and NiFe/Pt stacks and demonstrate robust and complete mutual synchronization of up to 21 nano-constrictions, reaching linewidths of below 200 kHz and quality factors beyond 79,000, while operating at 10 GHz. We also find a square increase in the peak power with the increasing number of mutually synchronized oscillators, resulting in a factor of 400 higher peak power in long chains compared to individual nano-constrictions. Although chains longer than 21 nano-constrictions also show complete mutual synchronization, it is not as robust and their signal quality does not improve as much as they prefer to break up into partially synchronized state

Surface acoustic waves (SAWs) convey energy at subwavelength depths along surfaces. Using interdigital transducers (IDTs) and opto-acousto-optic transducers (OAOTs), researchers have harnessed coherent SAWs with nanosecond periods and micrometer localization depth for various applications. However, the utilization of cutting-edge OAOTs produced through surface nanopatterning techniques has set the upper limit for coherent SAW frequencies below 100 GHz, constrained by factors such as the quality and pitch of the surface nanopattern, not to mention the electronic bandwidth limitations of the IDTs. In this context, unconventional optically-controlled nano-transducers based on cleaved superlattices (SLs) are here presented as an alternative solution. To demonstrate their viability, we conducted proof-of-concept experiments using ultrafast lasers in a pump-probe configuration on SLs made of alternating AlxGa1-xAs and AlyGa1-yAs layers with approximately 70 nm periodicity and cleaved along their growth direction to produce a periodic nanostructured surface. The acoustic vibrations, generated and detected by laser beams incident on the cleaved surface, span a range from 40 GHz to 70 GHz,

The advancements in nanotechnology, material science, and electrical engineering have shrunk the sizes of electronic devices down to the micro/nanoscale. This brings the opportunity of developing the Internet of Nano Things (IoNT), an extension of the Internet of Things (IoT). With nanodevices, numerous new possibilities emerge in the biomedical, military fields, and industrial products. However, a continuous energy supply is mandatory for these devices to work. At the micro/nanoscale, batteries cannot supply this demand due to size limitations and the limited energy contained in the batteries. Internet of Harvester Nano Things (IoHNT), a concept of Energy Harvesting (EH) integrated with wireless power transmission (WPT) techniques, converts the existing different energy sources into electrical energy and transmits to IoNT nodes. As IoHNTs are not directly attached to IoNTs, it gives flexibility in size. However, we define the size of IoHNTs as up to 10 cm. In this review, we comprehensively investigate the available energy sources and EH principles to wirelessly power IoNTs. We discuss the IoHNT principles, material selections, and state-of-the-art applications of each energy sour

Very recently, the papers "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof" by Jang and Ryu, and "The Iterates of Nesterov's Accelerated Algorithm Converge in the Critical Regimes" by Bot, Fadili, and Nguyen simultaneously have resolved a long-standing open problem concerning Nesterov's accelerated gradient method. These works show that the iterates of the algorithm (known in its composite form as FISTA) indeed converge to an optimal solution. In this work, we extend these results and prove that, in infinite dimensional Hilbert spaces, the iterates of such an algorithm still converge (in the weak sense) even when the proximity operator and the gradient are computed inexactly, with the latter possibly stochastic.

Regret matching (RM) -- and its modern variants -- is a foundational online algorithm that has been at the heart of many AI breakthrough results in solving benchmark zero-sum games, such as poker. Yet, surprisingly little is known so far in theory about its convergence beyond two-player zero-sum games. For example, whether regret matching converges to Nash equilibria in potential games has been an open problem for two decades. Even beyond games, one could try to use RM variants for general constrained optimization problems. Recent empirical evidence suggests that they -- particularly regret matching$^+$ (RM$^+$) -- attain strong performance on benchmark constrained optimization problems, outperforming traditional gradient descent-type algorithms. We show that RM$^+$ converges to an $ε$-KKT point after $O_ε(1/ε^4)$ iterations, establishing for the first time that it is a sound and fast first-order optimizer. Our argument relates the KKT gap to the accumulated regret, two quantities that are entirely disparate in general but interact in an intriguing way in our setting, so much so that when regrets are bounded, our complexity bound improves all the way to $O_ε(1/ε^2)$. From a technic

A superconducting quantum interference device (SQUID) miniaturized into nanoscale is promising in the inductive detection of a single electron spin. A nano-SQUID with a strong spin coupling coefficient, a low flux noise, and a wide working magnetic field range is highly desired in a single spin resonance measurement. Nano-SQUIDs with Dayem-bridge junctions excel in a high working field range and in the direct coupling from spins to the bridge. However, the common planar structure of nano-SQUIDs is known for problems such as a shallow flux modulation depth and a troublesome hysteresis in current-voltage curves. Here, we developed a fabrication process for creating three-dimensional (3-D) niobium (Nb) nano-SQUIDs with nano-bridge junctions that can be tuned independently. Characterization of the device shows up to 45.9 % modulation depth with a reversible current-voltage curve. Owning to the large modulation depth, the measured flux noise is as low as 0.34 μΦ$_0$/Hz$^{1/2}$. The working field range of the SQUID is greater than 0.5 T parallel to the SQUID plane. We believe that 3-D Nb nano-SQUIDs provide a promising step toward effective single-spin inductive detection.

Let $Φ'$ denote the strong dual of a nuclear space $Φ$ and let $C_{\infty}(Φ')$ be the collection of all continuous mappings $x:[0,\infty) \rightarrow Φ'$ equipped with the topology of local uniform convergence. In this paper we prove sufficient conditions for tightness of probability measures on $C_{\infty}(Φ')$ and for weak convergence in $C_{\infty}(Φ')$ for a sequence of $Φ'$-valued processes. We illustrate our results with two applications. First, we show the central limit theorem for local martingales taking values in the dual of an ultrabornological nuclear space. Second, we prove sufficient conditions for the weak convergence in $C_{\infty}(Φ')$ for a sequence of solutions to stochastic partial differential equations driven by semimartingale noise.

Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user, regardless of the initial condition. Furthermore, such a class of controllers has been shown to maintain a prescribed-time convergence in the presence of disturbances even if the disturbance bound is unknown. However, such properties require a time-varying gain that becomes singular at the terminal time, which limits its application to scenarios under quantization or measurement noise. This chapter presents a methodology to design a broader class of controllers, called predefined-time controllers, with a prescribed convergence-time bound. Our approach allows designing robust predefined-time controllers based on time-varying gains while maintaining uniformly bounded time-varying gains. We analyze the condition for uniform Lyapunov stability under the proposed time-varying controllers.

We have performed scanning angle-resolved photoemission spectroscopy with a nanometer-sized beam spot (nano-ARPES) on the cleaved surface of Pb5Bi24Se41, which is a member of the (PbSe)5(Bi2Se3)3m homologous series (PSBS) with m = 4 consisting of alternate stacking of the topologically-trivial insulator PbSe bilayer and four quintuple layers (QLs) of the topological insulator Bi2Se3. This allows us to visualize a mosaic of topological Dirac states at a nanometer scale coming from the variable thickness of the Bi2Se3 nano-islands (1-3 QLs) that remain on top of the PbSe layer after cleaving the PSBS crystal, because the local band structure of topological origin changes drastically with the thickness of the Bi2Se3 nano-islands. A comparison of the local band structure with that in ultrathin Bi2Se3 films on Si(111) gives us further insights into the nature of the observed topological states. This result demonstrates that nano-ARPES is a very useful tool for characterizing topological heterostructures.

The spatially precise integration of arrays of micro-patterned two-dimensional (2D) crystals onto three-dimensionally structured Si/SiO$_2$ substrates represents an attractive strategy towards the low-cost system-on-chip integration of extended functions in silicon microelectronics. However, the reliable integration of the arrays of 2D materials on non-flat surfaces has thus far proved extremely challenging due to their poor adhesion to underlying substrates as ruled by weak van der Waals interactions. Here we report on a novel fabrication method based on nano-subsidence which enables the precise and reliable integration of the micro-patterned 2D materials/silicon photodiode arrays exhibiting high uniformity. Our devices display peak sensitivity as high as 0.35 A/W and external quantum efficiency (EQE) of ca. 90%, outperforming most commercial photodiodes. The nano-subsidence technique opens a viable path to on-chip integrate 2D crystals onto silicon for beyond-silicon microelectronics.

Recently, much progress has been made on particle swarm optimization (PSO). A number of works have been devoted to analyzing the convergence of the underlying algorithms. Nevertheless, in most cases, rather simplified hypotheses are used. For example, it often assumes that the swarm has only one particle. In addition, more often than not, the variables and the points of attraction are assumed to remain constant throughout the optimization process. In reality, such assumptions are often violated. Moreover, there are no rigorous rates of convergence results available to date for the particle swarm, to the best of our knowledge. In this paper, we consider a general form of PSO algorithms, and analyze asymptotic properties of the algorithms using stochastic approximation methods. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le \gm<0$), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than $2+|\gm|$. For the usual $L^1$-convergence we prove that the convergence rate can be controlled from below by the initial energy tails, and hence, for initial data with long energy tails, the convergence can be arbitrarily slow. We also show that under the integrable angular cutoff on the collision kernel with $-1\le \gm<0$, there are algebraic upper and lower bounds on the rate of $L^1$-convergence to equilibrium. Our methods of proof are based on entropy inequalities and moment estimates.

Recent advances in nanotechnology have created tremendous excitement across different disciplines but in order to fully control and manipulate nano-scale objects, we must understand the forces at work at the nano-scale, which can be very different from those that dominate the macro-scale. We show that there is a new kind of curvature-induced force that acts between nano-corrugated electrically neutral plasmonic surfaces. Absent in flat surfaces, such a force owes its existence entirely to geometric curvature, and originates from the kinetic energy associated with the electron density which tends to make the profile of the electron density smoother than that of the ionic background and hence induces curvature-induced local charges. Such a force cannot be found using standard classical electromagnetic approaches, and we use a self-consistent hydrodynamics model as well as first principles density functional calculations to explore the character of such forces. These two methods give qualitative similar results. We found that the force can be attractive or repulsive, depending on the details of the nano-corrugation, and its magnitude is comparable to light induced forces acting on pla

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic notions which have been applied to study sequences of submanifolds in Euclidean space: Hausdorff convergence of sets, flat convergence of integral currents, and weak convergence of varifolds. We next describe a variety of intrinsic notions of convergence which have been applied to study sequences of compact Riemannian manifolds: Gromov-Hausdorff convergence of metric spaces, convergence of metric measure spaces, Instrinsic Flat convergence of integral current spaces, and ultralimits of metric spaces. We close with a speculative section addressing possible notions of intrinsic varifold convergence, convergence of Lorentzian manifolds and area convergence.

Spin-wave based transmission and processing of information is a promising emerging nano-technology that can help overcome limitations of traditional electronics based on the transfer of electrical charge. Among the most important challenges for this technology is the implementation of spin-wave devices that can operate without the need for an external bias magnetic field. Here we experimentally demonstrate that this can be achieved using sub-micrometer wide spin-wave waveguides fabricated from ultrathin films of low-loss magnetic insulator - Yttrium Iron Garnet (YIG). We show that these waveguides exhibit a highly stable single-domain static magnetic configuration at zero field and support long-range propagation of spin waves with gigahertz frequencies. The experimental results are supported by micromagnetic simulations, which additionally provide information for optimization of zero-field guiding structures. Our findings create the basis for the development of energy-efficient zero-field spin-wave devices and circuits.

The property that the velocity $\boldsymbol{u}$ belongs to $L^\infty(0,T;L^2(Ω)^d)$ is an essential requirement in the definition of energy solutions of models for incompressible fluids. It is, therefore, highly desirable that the solutions produced by discretisation methods are uniformly stable in the $L^\infty(0,T;L^2(Ω)^d)$-norm. In this work, we establish that this is indeed the case for Discontinuous Galerkin (DG) discretisations (in time and space) of non-Newtonian models with $p$-structure, assuming that $p\geq \frac{3d+2}{d+2}$; the time discretisation is equivalent to the RadauIIA Implicit Runge-Kutta method. We also prove (weak) convergence of the numerical scheme to the weak solution of the system; this type of convergence result for schemes based on quadrature seems to be new. As an auxiliary result, we also derive Gagliardo-Nirenberg-type inequalities on DG spaces, which might be of independent interest.

In most of the cases, the experimental study of Nanotechnology involves high cost for Laboratory set-up and the experimentation processes were also slow. So, one cannot rely on experimental nanotechnology alone. As such, the Computer-Based molecular simulations and modeling are one of the foundations of computational nanotechnology. The computer based modeling and simulations were also referred as computational experimentations. In real experiments, the investigator doesn't have full control over the experiment. But, in Computational experimentation the investigator have full control over the experiment. The accuracy of such Computational nano-technology based experiment generally depends on the accuracy of the following things: Intermolecular interaction, Numerical models and Simulation schemes used. Once the accuracy of the Computational Scheme is guaranteed one can use that to investigate various nonlinear interactions whose results are completely unexpected and unforeseen. Apart from it, numerical modeling and computer based simulations also help to understand the theoretical part of the nano-science involved in the nano-system. They allow us to develop useful analytic and pred

Scalable memories that can match the speeds of superconducting logic circuits have long been desired to enable a superconducting computer. A superconducting loop that includes a Josephson junction can store a flux quantum state in picoseconds. However, the requirement for the loop inductance to create a bi-state hysteresis sets a limit on the minimal area occupied by a single memory cell. Here, we present a miniaturized superconducting memory cell based on a Three-Dimensional (3D) Nb nano-Superconducting QUantum Interference Device (nano-SQUID). The major cell area here fits within an 8*9 μm^2 rectangle with a cross-selected function for memory implementation. The cell shows periodic tunable hysteresis between two neighbouring flux quantum states produced by bias current sweeping because of the large modulation depth of the 3D nano-SQUID (~66%). Furthermore, the measured Current-Phase Relations (CPRs) of nano-SQUIDs are shown to be skewed from a sine function, as predicted by theoretical modelling. The skewness and the critical current of 3D nano-SQUIDs are linearly correlated. It is also found that the hysteresis loop size is in a linear scaling relationship with the CPR skewness