Order Dispersion Research Articles

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Impact of higher order dispersion in the propagation of optical pulse in the photonic crystal fibers - A Projection Operator approach

Impact of higher order dispersion in the propagation of optical pulse in the photonic crystal fibers - A Projection Operator approach

Method for Controlling Dispersion in Order to Maintain a Quasi-Soliton Pulse Propagation Mode in High-Speed Fiber-Optic Communications System

Relevance: Every year, there is an increasing need to enhance the bandwidth and range of fiber-optic communication systems. The study of methods to control dispersion is relevant and helps maintain a quasi-soliton regime, which is essential for ensuring high-speed, reliable data transmission. Conducted modeling and calculations make this research practical and applicable. This will enable engineers to accurately predict the system's behavior and optimize its performance before implementing it in real-world networks.Problem statement: Investigation of the processes of maintaining a quasi-soliton regime in fibers with decreasing chromatic dispersion and alternating fibers with different signs of chromatic dispersion, both with and without initial chirping.Goal of the work: The development and analysis of techniques to control dispersion in order to maintain a quasi-soliton mode of light propagation in single-mode optical fibers.Methods: The study of the processes of maintaining a quasi-soliton regime was carried out by mathematical and numerical modeling. To substantiate the methods, theoretical analysis and calculations were carried out and schemes for a quasi-soliton fiber-optic communication system were developed and modeling was carried out.Result: The analysis of the results demonstrated the effectiveness of the proposed method and showed the efficiency and stability of the solutions in conditions that were close to real-world scenarios. Novelty: Models for maintaining a quasi-soliton regime and methods for studying them have been developed. The most effective ways to preserve quasi-soliton pulses over long distances have been analyzed.Practical significance: The developed models and research methods can be applied in the educational process and the development of real fiber-optic communication systems.

M-shaped, W-shaped and dark soliton propagation in optical fiber for nonlocal fourth order dispersive nonlinear Schrödinger equation under distinct conditions

The formation of soliton in optical fiber governed by nonlocal nonlinear Schrödinger (NLS) equation with fourth order dispersion is studied. The model of nonlocal NLS equation with fourth order dispersion is solved using the new extended auxiliary method and the solutions are obtained. The solutions are in the form of hyperbolic and trigonometric functions which are based on Jacobi elliptic function m. Shape changing soliton in optical fiber for nonlocal fourth order dispersive NLS equation is discussed by suitably choosing the values of kerr and quintic nonlinearities and by varying fourth order dispersion term. The effect of fourth order dispersion on soliton in fiber for different conditions of kerr and quintic nonlinearity is also discussed. In addition, the phase portraits of the system have been investigated and the stability of wave in optical fiber for nonlocal NLS equation is discussed using fourth order Runge-Kutta algorithm. This paper addresses a significant gap in the current literature by examining the impact of fourth order dispersion on the nonlocal NLS equation in optical fiber.

Circular code identified by the codon usage

Since 1996, circular codes in genes have been identified thanks to the development of 6 statistical approaches: trinucleotide frequencies per frame (Arquès and Michel, 1996), correlation functions per frame (Arquès and Michel, 1997), frame permuted trinucleotide frequencies (Frey and Michel, 2003, 2006), advanced statistical functions at the gene population level (Michel, 2015) and at the gene level (Michel, 2017). All these 3-frame statistical methods analyse the trinucleotide information in the 3 frames of genes: the reading frame and the 2 shifted frames. Notably, codon usage does not allow for the identification of circular codes (Michel, 2020). This has been a long-standing problem since 1996, hindering biologists’ access to circular code theory.By considering circular code conditions resulting from code theory, particularly the concept of permutation class, and building upon previous statistical work, a new statistical approach based solely on the codon usage, i.e. a 1-frame statistical method, surprisingly reveals the maximal C3 self-complementary trinucleotide circular code X in bacterial genes and in average (bacterial, archaeal, eukaryotic) genes, and almost in archaeal genes. Additionally, a new parameter definition indicates that bacterial and archaeal genes exhibit codon usage dispersion of the same order of magnitude, but significantly higher than that observed in eukaryotic genes. This statistical finding may explain the greater variability of codes in eukaryotic genes compared to bacterial and archaeal genes, an issue that has been open for many years. Finally, biologists can now search for new (variant) circular codes at both the genome level (across all genes in a given genome) and the gene level using only codon usage, without the need for analysing the shifted frames.

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

Our study delves into the intricate interplay of various factors within metamaterials, with a focus on modulation instability. Through our research, we elucidate the intricate dynamics involving intermodal dispersion, self-steepening effect, higher order dispersion, and plane wave amplitude, showcasing their competition and influence on modulation instability phenomena. We aim to explore the impact of intermodal dispersion and higher-order effects by numerically solving the generalized nonlinear Schrödinger equation (NLSE), which models the propagation of a few-cycle pulse in a nonlinear metamaterial. Our modulation instability (MI) analysis captures the complex dynamics these factors introduce. We demonstrate the spatiotemporal evolution of MI under different parameter values, revealing how these variations influence the instability’s development and characteristics. This approach provides a detailed understanding of the system’s behavior across various conditions, highlighting the roles of intermodal dispersion and higher-order effects. We demonstrate that the behavior of modulation instability bands and their reliance on parameters such as self-steepening and wave amplitude is contingent upon the specific characteristics of the optical setup and medium dispersion properties

Transmission of soliton for a coupled Radhakrishnan–Kundu–Lakshmanan equation in an optical fiber using the Jacobi elliptical sn function method

We examine a coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) equation that includes self-phase modulation, third order dispersion, self-steepening, and cross-phase modulation effects. A propagating ultrafast pulse in nonlinear systems is described by the given equation. Utilizing the coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) model, we explored the dynamics of various innovative optical solitons, such as wing-shaped, W-shaped, and brilliant solitons. We used mathematical methods like the Jacobi elliptical sn function method to get the exact analytical solution. Our results demonstrate that the self-phase modulation (SPM), self-steepening (SS), cross-phase modulation (XPM), and third order dispersion (TOD) can be effectively varied to influence the structure of the solitons. It is demonstrated that the precise balance between the self-steepening effect, the self-phase modulation, and the group velocity dispersion forms these novel W-shaped chirp-free dark solitons and dark and bright solitonic structures. By choosing appropriate settings for the physical variables, it is possible to create a graphic representation of the properties of optical solitons. The study and application of nonlinear materials with third order dispersion, cross-phase modulation, self-phase modulation effect, and self-steepening nonlinearity may take new paths as a result of our findings.

Accurate optical dispersion identification for linear deformable mirror with spatial-spectral interferometry

In ultrashort laser pulse systems, optical dispersion can cause severe distortion of the spectral phase and thus significantly affect the pulse shape. To address this problem, this study places a linear deformable mirror (LDM) at the Fourier plane of a blazed grating for dispersion control, and reconstructs the spectral phase modulated by the LDM using single-shot spatial-spectral interferometry. An iterative algorithm and closed-loop optimization process are used to drive the LDM to generate orthogonal modes of Legendre polynomials with a signal-to-background ratio (SBR) of more than 10 dB. The identified LDM modes are then used as the basis for spectral phase modulation. It is shown that the group delay dispersion (GDD), third order dispersion (TOD), fourth order dispersion (FOD), and fifth order dispersion (5OD) can be accurately obtained by the linear combination of identified Legendre modes. In addition, the maximum phase error between the generated and target dispersions is less than 0.15 rad, while the error between the pulse widths produced by the generated dispersion and the target dispersion, respectively, is less than 3.5 %. Overall, the results confirm that the linear superposition of the generated Legendre modes enables the accurate dispersion modulation of ultrashort laser pulses.

Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion

Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion

Dynamics of switching optical soliton in fiber with sixth order dispersion and inter modal dispersion

This work pertains to the study of switching soliton in fiber for nonlinear Schrödinger (NLS) equation with the presence of higher order dispersion and inter modal dispersion (IMD). The nonlinear wave in the optical fiber are described by the NLS equation which having the second order, fourth order, fifth order, sixth order dispersion, higher order nonlinearity and IMD. The main goal of the paper is to examine the sixth order dispersion on nonlinear wave in the fiber with the conditions of IMD. Hence, we employ the Bäcklund transformation of the Riccati equation (BTRE) approach to NLS equation and obtain the soliton solution. By the use of soliton solution along with graphical snapshots, we provide the conditions for forming switching solition in optical fiber and also analyze the effect of sixth order dispersion in fiber. The stability of the solution of NLS equation is also addressed.

Analysis of performance limits in optical communications due to fiber nonlinearity and third order dispersion

In this study, an analysis is conducted to treasure the expressions of the pulsation expansion factor, in addition to the standardized output, and solve the nonlinear Schrödinger equation (NLSE), reflecting the impact of XPM on third order dispersion. Using large effective area fiber (LEAF) and standard single-mode fiber (SSMF), the effects of transmission distances and varying input powers are assessed at various transmission speeds. The first and second order GVD XPM effects are the only factors influencing the pulse’s propagation. The second-order effects of GVD are not noticeable at short distances and low bit rates, but they become noticeable and impact system performance as the bit rate increases. The study discovered that input dominance has less of an impact on pulse width than data rate and fiber length. Methodical derivation and numerical simulation using the split-phase Fourier method at the same data rate and input power yield the SSMF and LEAF consequences. In comparison to LEAF fibers, XPM has a greater beneficial impact on second and third order dispersion in SSMF fibers.

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

Enhanced antichemobrain activity of amino acid assisted ferulic acid solid dispersion in adult zebrafish (Danio rerio).

Chemotherapy-induced cognitive impairment (CICI), also known as "chemobrain," is a common side effect of breast cancer therapy which causes oxidative stress and generation of reactive oxygen species (ROS). Ferulic acid (FA), a natural polyphenol, belongs to BCS class II is confirmed to have nootropic, neuroprotective and antioxidant effects. Here, we have developed FA solid dispersion (SD) in order to enhance its therapeutic potential against chemobrain. An amorphous ferulic acid loaded leucin solid dispersion (FA-Leu SD) was prepared by utilizing amino acid through spray-drying technique. The solid-state characterization was carried out via Fourier-transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), X-ray diffraction (XRD), and field emission scanning electron microscopy (FE-SEM). Additionally, in-vitro release studies and antioxidant assay were also performed along with in-vivo locomotor, biochemical and histopathological analysis. The physical properties showed that FA-Leu SD so formed exhibited spherical, irregular surface hollow cavity of along with broad melting endotherm as observed from FE-SEM and DSC results. The XRD spectra demonstrated absence of sharp and intense peaks in FA-Leu SD which evidenced for complete encapsulation of drug into carrier. Moreover, in-vitro drug release studies over a period of 5h in PBS (pH 7.4) displayed a significant enhanced release in the first hr (68. 49 ± 5.39%) and in-vitro DPPH assay displayed greater antioxidant potential of FA in FA-Leu SD. Furthermore, the in-vivo behavioral findings of FA-Leu SD (equivalent to 150mg/kg of free FA) exhibited positive results accompanied by in-vivo biochemical and molecular TNF-α showed a significant difference (p < 0.001) vis-à-vis DOX treated group upon DOX + FA-Leu SD. Additionally, histopathological analysis revealed neuroprotective effects of FA-Leu SD together with declined oxidative stress due to antioxidant potential of FA which was induced by anticancer drug doxorubicin (DOX). Overall, the above findings concluded that spray-dried FA-Leu SD could be useful for the treatment of chemotherapy induced cognitive impairment.

Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion

Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion

Approximate controllability of third order dispersion systems

The current paper focuses on the approximate controllability of Volterra-Fredholm type integrodifferential third order dispersion system. The Banach fixed point theorem and semigroup operator are used to obtain the existence and uniqueness of mild solutions to the considered system. In order to examine the approximate controllability results, a different approach is used, namely, the sequential method.

Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes

&lt;abstract&gt;&lt;p&gt;This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schrödinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schrödinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algorithms are implemented to investigate the optical solitons with the governing model. These techniques are the Weierstrass-type projective Riccati equation expansion method, the addendum to Kudryashov's method, and the new mapping method. The solutions obtained include various solitons, such as bright, dark, and straddled solitons. Additionally, the paper reports hyperbolic solutions and Weierstrass-type doubly periodic solutions. These solutions are novel and have never been reported before. Visual depictions of some selected solitons illustrate these solutions' dynamic behavior and wave structure.&lt;/p&gt;&lt;/abstract&gt;

Studying effects of emissions from thermal power plants on ambient air quality in Cam Pha city

The article presents some research results on assessing emissions from the chimneys of Cam Pha, Mong Duong 1 and Mong Duong 2 thermal power plants through comparison of the concentrations of TSP, SO2 and NOx with national and local standards on industrial emissions (QCVN 22:2009/BTNMT, QCDP 5:2020/QN), and applying AERMOD VIEW 10.2.1 software to simulate pollutant dispersions in order to evaluate the effects of this emission on ambient air quality in Cam Pha city. The research results show that at several times, the emission concentrations of all three parameters of TSP, NOx và SO2 were higher than standard values, with the maximum frequencies of exceeding standard were 2,79%, 25,92% and 8%, respectively. The maximum levels of exceeding standard were 4,29 times for TSP, 4,04 times for NOx and 7,17 times for SO2. The research results also indicate that there is a place where the hourly average concentration of NO2 is 2.7 times higher than the local standard QCDP 4:2020/QN on ambient air quality. The simulation results of pollutant dispersions showed that the area in the west-northwest of Mong Duong 1 and 2 thermal power plants has concentrations of SO2 and NO2 (hourly average) exceeding the current allowable standards.

Study of Soliton Interaction in Optical Fibers with Third Order Dispersion and Higher Order Nonlinear Effects

In this paper, we present a numerical approach to solve the GNLSE and analyze soliton interaction phenomena using COMSOL environment. By leveraging the capabilities of COMSOL's PDE module, we can accurately capture the dynamics of solitons and investigate their interactions. We analyze the impact of different parameters such as soliton power, initial separation distance, and dispersion characteristics on the soliton dynamics. Furthermore, we examine the role of higher-order dispersion terms in shaping the soliton interactions. Our findings demonstrate the effectiveness of the proposed numerical approach in accurately simulating and analyzing soliton interaction phenomena. The COMSOL-based methodology provides a flexible and efficient framework for studying complex nonlinear optical systems, enabling researchers to gain insights into the behavior of solitons in different media and design optimized communication systems. This paper contributes to the understanding of soliton dynamics and provides a practical tool for investigating the behavior of solitons in nonlinear dispersive media. The presented numerical approach using COMSOL opens avenues for further research in nonlinear optics and fiber optic communication systems.

Integrated schedule of order picking and delivery for instant delivery

In this study, we introduce an integrated schedule of order picking and delivery for instant delivery. Order picking, including order batching and picking sequencing, is scheduled online under real-time order arrival, which integrates order delivery by depicting order location dispersion in an online order picking strategy. Order delivery, including delivery person assignment and route planning, is modeled to minimize the total duration of order fulfillment by considering the influence of the order picking completion time. A rule-based online order picking strategy is established, and a customized ant colony optimization (ACO) algorithm is proposed to optimize order delivery. Experiments on 16 simulated instances of different scales demonstrate that our online order picking schedule considering order delivery outperforms existing approaches and that the customized ACO algorithm for order delivery is effective.

On the persistence of spatial analyticity for generalized KdV equation with higher order dispersion

AbstractPersistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersion where , are integers. For a class of analytic initial data with a fixed radius of analyticity , we show that the uniform radius of spatial analyticity of solutions at time cannot decay faster than as . In particular, this improves a recent result due to Petronilho and Silva [Math. Nachr. 292 (2019), no. 9, 2032–2047] for the modified Kawahara equation (, ), where they obtained a decay rate of order . Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates.