One-dimensional Systems Research Articles

Efficiency of neural-network state representations of one-dimensional quantum spin systems

Neural-network state representations of quantum many-body systems are attracting great attention and more rigorous quantitative analysis of their expressibility and complexity is warranted. Our analysis of the restricted Boltzmann machine (RBM) state representation of one-dimensional (1D) quantum spin systems provides new insight into their computational complexity. We define a class of long-range-fast-decay (LRFD) RBM states with quantifiable upper bounds on truncation errors and provide numerical evidence for a large class of 1D quantum systems that may be approximated by LRFD RBMs of at most polynomial complexities. These results lead us to conjecture that the ground states of a wide range of quantum systems may be exactly represented by LRFD RBMs or a variant of them, even in cases where other state representations become less efficient. At last, we provide the relations between multiple typical state manifolds. Our work proposes a paradigm for doing complexity analysis for generic long-range RBMs which naturally yields a further classification of this manifold. This paradigm and our characterization of their nonlocal structures may pave the way for understanding the natural measure of complexity for quantum many-body states described by RBMs and are generalizable for higher-dimensional systems and deep neural-network quantum states. Published by the American Physical Society 2024

Development of the thermal hydraulic analysis code, TASS/SMR-S, under multi-dimensional motion for a reactor under inclination and rolling conditions

The development of a thermal hydraulic analysis code that considers ship motion is important because it would adjust for additional motion effects that are not present in a land-based system analysis code. The TASS/SMR-S code, a one-dimensional system analysis code, was modified to predict the thermal hydraulic behavior of a nuclear reactor under the conditions of an ocean environment. To validate the improved TASS/SMR-S code, the calculation results were compared with the analytical solutions for a conceptual problem involving swaying, rolling, and compounded motions; experimental data were collected under inclination and rolling conditions. The modified TASS/SMR-S code exhibited good agreement with analytical solutions for the conceptual problem and experimental results obtained under ship motion conditions. In conclusion, the modified code was able to simulate thermal hydraulic behavior under ship motion conditions.

Enhanced Drude weight in a one-dimensional system of fermions with pair-hopping events

Enhanced Drude weight in a one-dimensional system of fermions with pair-hopping events

Tuning the diffusion constant to optimize the readout of the positional information of spatial concentration patterns

Abstract Positional information encoded in spatial concentration patterns is crucial for the development of multicellular organisms. However, it is still unclear how such information is affected by the physically dissipative diffusion process. Here we study one-dimensional patterning systems with analytical derivation and numerical simulations. We find that the diffusion constant of the patterning molecules exhibits a nonmonotonic effect on the readout of the positional information from the concentration patterns. Specifically, there exists an optimal diffusion constant that maximizes the positional information. Moreover, we find that the energy dissipation due to the physical diffusion imposes a fundamental upper limit on the positional information.

Density functional theory study of the electronic and optical properties of pentagraphyne nanotubes.

Pentagraphyne (PG-yne), a recently predicted two-dimensional (2D) carbon allotrope with appealing properties, has opened up possibilities for a wide range of applications. In this study, we investigate the structural, electronic, optical, and electrical transport properties of a novel one-dimensional (1D) system called pentagraphyne nanotubes (PG-yneNTs), formed by rolling a PG-yne sheet, using density functional theory (DFT) calculations. We design PG-yneNTs with diameters ranging from 6.94 Å to 13.62 Å and employ state-of-the-art theoretical calculations to confirm their energetic, dynamic, and thermodynamic stability. Our electronic band structure calculations reveal that all these nanotubes are wide indirect band gap semiconductors. Remarkably, PG-yneNTs exhibit superior optical properties, including high absorption coefficients and absorption spectra covering the visible regime of the electromagnetic spectrum, making them potential candidates for visible-light-driven photocatalysis and solar cells. Interestingly, both the electronic and optical band gaps increase with the diameter of the nanotubes. Additionally, the observation of negative differential resistance (NDR) phenomena in (4, 0) PG-yneNT suggests their potential applications in NDR devices such as fast switches, frequency multipliers, and memory devices.

Lie Symmetry Analysis, Power Series Solutions and Conservation Laws of (2+1)-Dimensional Time Fractional Modified Bogoyavlenskii–Schiff Equations

In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is utilized to reduce the system of (2+1)-dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to the system of (1+1)-dimensional fractional partial differential equations with Erdélyi–Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

The Attention-Based Autoencoder for Network Traffic Classification with Interpretable Feature Representation

Network traffic classification is crucial for identifying network applications and defending against network threats. Traditional traffic classification approaches struggle to extract structural features and suffer from poor interpretability of feature representations. The high symmetry between network traffic classification and its interpretable feature representation is vital for network traffic analysis. To address these issues, this paper proposes a traffic classification and feature representation model named the attention mechanism autoencoder (AMAE). The AMAE model extracts the global spatial structural features of network traffic through attention mechanisms and employs an autoencoder to extract local structural features and perform dimensionality reduction. This process maps different network traffic features into one-dimensional coordinate systems in the form of spectra, termed FlowSpectrum. The spectra of different network traffic represent different intervals in the coordinate system. This paper tests the interpretability and classification performance of network traffic features of the AMAE model using the ISCX-VPN2016 dataset. Experimental results demonstrate that by analyzing the overall distribution of attention weights and local weight values of network traffic, the model effectively explains the differences in the spectral representation intervals of different types of network traffic. Furthermore, our approach achieves the highest classification accuracy of up to 100% for non-VPN-encrypted traffic and 99.69% for VPN-encrypted traffic, surpassing existing traffic classification schemes.

Van der Waals Engineering of Charge Density Waves in One-Dimensional Nb6Te6 Nanowires.

One-dimensional (1D) systems have played a crucial role in the development of fundamental physics and practical applications. Recently, transition metal monochalcogenide (TMM) wires based on molybdenum (Mo) and tungsten (W) have emerged as promising platforms for investigating 1D physics in pure van der Waals (vdW) platforms. Here, we report on the bottom-up fabrication of Nb6Te6 wires down to the single-wire limit. The unique properties of Nb6Te6 single wire enable the realization of 1D charge density wave (CDW) phases in an isolated single TMM wire. Moreover, we revealed the appealing regulation of 1D CDW orders by van der Waals interactions at either the 1D-2D interface (i.e., rotation of a single wire along its wire axis) or the 1D-1D interface. Two rotation angles (30° and 0°) give rise to 3 × 1 and zigzag chain CDW morphologies, respectively, which exhibit pronounced differences in atomic displacement by a factor of 2. The interwire vdW coupling overwhelms its counterpart at the 1D-2D interface, thus locking the rotation angle (at 0°) as well as the interwire atomic registries. In contrast, interestingly, the phases of the charge oscillations are independent of the adjacent wires. The ability to tailor 1D charge orders provides a crucial addition to the toll set of vdW integrations beyond two-dimensional materials.

New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type

In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the best of our knowledge, explicit and general energy decay rates for this system with infinite memory. We use Sobolev embedding and the multiplier approach to get our decay results. These results generalize and improve some earlier related results in the literature.

Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment

In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.

A powerful tool for dealing with high-dimensional fractional-order systems with applications to fractional Emden–Fowler systems

In this study, an approximation solution for a high-dimensional system in terms of the Caputo fractional derivative operator is obtained using the improved modified fractional Euler method, or IMFEM for short. To accomplish this aim, a result that can transform such a system into a double-equation, one-dimensional fractional-order system, is provided theoretically. Some physical applications, including fractional-order systems of equations of Emden–Fowler type, are discussed, and their graphs are plotted using MATLAB to demonstrate the IMFEM schema’s validity.

Local bit-level image encryption algorithm based on one dimensional zero excluded chaotic map

The exchange of digital images on the internet has become more convenient, but it has also led to increasing security concerns. Image encryption differs from text encryption, as inherent features such as massive data volume and high pixel correlation make it challenging to apply traditional AES and DES methods to images. This paper introduces a novel local bit-level image encryption algorithm based on chaos. Firstly, a new one-dimensional chaos system named the One-Dimensional Zero Excluded Chaotic Map (1D-ZECM) is designed, possessing features such as approximate global chaos, a broad chaos range, and high Lyapunov exponents, making it well-suited for cryptography. To resist brute force attacks, a hash function is employed to generate the encryption system’s key, further enhanced by using the 1D-ZECM to derive the key stream for the cryptographic system. Unlike traditional encryption methods that encrypt all 8 bits of a pixel, this algorithm focuses on the first six bits of each pixel during the encryption process, as the lower two bits contain less image information. In the diffusion process, the key stream generated by the 1D-ZECM is combined with mod and XOR operations to diffuse the rearranged image. Experimental results demonstrate that the proposed encryption algorithm exhibits high security and can resist common attacks. Moreover, when compared to representative algorithms, the proposed algorithm demonstrates better security and efficiency. The encryption algorithm presented in this paper provides a high-quality encrypted output.

Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to 1/2 in propagating-propagating and (de)localization transitions.

Statistical physics of frictional grains: Some simple applications of the Edwards statistics

Granular matter like sand is composed of a large number of interacting grains and is, thus, expected to be amenable to a statistical physics treatment. Yet, the frictional properties of grains make the statistical physics of granular matter significantly different from the equilibrium statistical physics of atomic or molecular systems. We use three simple models to illustrate some of the key concepts of the statistical physics introduced by Edwards and co-workers more than 30 years ago to describe shaken granular piles: non-interacting frictional grains attached to a wall by a spring, a chain of frictional grains connected by springs, and a simplified mean-field model of a granular packing. We observe that a chain of frictional grains connected by springs exhibits a critical point at an infinite effective temperature (i.e., infinitely strong shaking) at odds with the zero-temperature critical point generically found in one-dimensional systems at thermal equilibrium in the presence of local interactions.

Coprime Factor Model Reduction of Multidimensional Systems

In this work, the right coprime factor for balancing and truncating unstable systems is extended to parameter-varying multidimensional systems employing recent works on coprime factor model reduction of one-dimensional uncertain systems. Since the balanced truncation method cannot be applied directly to unstable systems, state feedback gains should be computed and incorporated in order to stabilize the given system and to be able to apply the balanced truncation technique via defining the so-called stable coprime factor, as coprime factorization overcomes the stability condition required for model reduction. Parameter-dependent state feedback and parameter-dependent Gramians are considered in this work yielding less conservative techniques. In addition, the Gramians are defined as block diagonal matrices, which are partitioned according to the structure of the multidimensional systems. The application to a simulation example demonstrates the applicability and validity of the proposed reduction approach leading to small error bounds between the full and the reduced models.

Activity-induced ferromagnetism in one-dimensional quantum many-body systems

Activity-induced ferromagnetism in one-dimensional quantum many-body systems

Quantum transport regimes in quartic dispersion materials with Anderson disorder

Mexican-hat-shaped quartic dispersion manifests itself in certain families of single-layer two-dimensional hexagonal crystals such as compounds of groups III–VI and groups IV–V as well as elemental crystals of group V. A quartic band forms the valence band edge in various of these structures, and some of the experimentally confirmed structures are GaS, GaSe, InSe, SnSb, and blue phosphorene. Here, we numerically investigate strictly one-dimensional and quasi-one dimensional (Q1D) systems with quartic dispersion and systematically study the effects of Anderson disorder on their transport properties with the help of a minimal tight-binding model and Landauer formalism. We compare the analytical expression for the scaling function with simulation data to distinguish the domains of diffusion and localization regimes. In one dimension, it is shown that conductance drops dramatically at the quartic band edge compared to the quadratic case. As for the Q1D nanoribbons, a set of singularities emerge close to the band edge, suppressing conductance and leading to short mean-free-paths and localization lengths. Interestingly, wider nanoribbons can have shorter mean-free-paths because of denser singularities. However, the localization lengths sometimes follow different trends. Our results display the peculiar effects of quartic dispersion on transport in disordered systems.

Determination of the Speed and Surface Temperature of Aircraft Using the Second Approximation of the System of Moment Equations

This study focuses on solving the initial-boundary value problem for a one-dimensional non-stationary nonlinear system of moment equations in the second approximation. We prove the existence of a unique local in-time solution of the problem under consideration in the space of functions that are continuous in time and square integrable over the spatial variable x. To solve the direct and inverse problems for this system, we develop an iterative numerical method and reduce the system of moment equations to canonical form. Furthermore, we present the software implementation of the algorithms and their application for solving inverse problems related to determining the speed and surface temperature of an aircraft, as well as atmospheric parameters. We provide the results of numerical experiments conducted to validate our approach.

Universal stability of coherently diffusive one-dimensional systems with respect to decoherence

Universal stability of coherently diffusive one-dimensional systems with respect to decoherence

Medical image encryption system based on a simultaneous permutation and diffusion framework utilizing a new chaotic map

In telemedicine, diverse medical images transmitted between doctors and patients contain sensitive personal information. Thus, there is an urgent need for reliable and efficient medical image encryption to protect these medical images during transmission. In this paper, a simultaneous permutation and diffusion framework (SPDF) is introduced for medical image encryption based on a new chaotic map. Firstly, combining the Chebyshev map and the iterative chaotic map with infinite collapse (ICMIC), we propose a one-dimensional chaotic system (1D-CICMIC) which exhibits higher ergodicity and unpredictability compared to other 1D chaotic maps through comprehensive analyses. Secondly, in order to enhance permutation effect, we modify traditional Josephus traversing with a dynamic scrambling method where the scrambling scheme of the current pixel depends on the value of the previous diffused pixel. Thirdly, we develop a simultaneous permutation and diffusion framework, wherein the diffusion is embedded into the modified Josephus traversing to prevent attackers from targeting the scrambling and diffusion phases separately. Finally, based on 1D-CICMIC and SPDF, an encryption system is proposed. It adopts plaintext correlation in the diffusion operation, which strikes a balance between ciphertext sensitivity and plaintext sensitivity, offering resistance against chosen-plaintext attack (CPA), noise attack and data loss. Simulation results show that the proposed algorithm has high encryption efficiency and can withstand various common attacks.