International Journal of Modern Physics B

This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this field in China so the references, therefore, are not exhaustive.

We study a new kind of ordering — topological order — in rigid states (the states with no local gapless excitations). We concentrate on characterization of the different topological orders. As an example we discuss in detail chiral spin states of 2 + 1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. We show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. We also discuss the symmetry properties of the degenerate ground states of chiral spin states. We find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90° rotation.

The dynamical theory of the edge excitations of generic fractional quantum Hall (FQH) states is summarized and expanded. The low energy effective theory of the edge excitations for the most general abelian FQH states (including spin-unpolarized and multi-layer FQH states) and some non-abelian FQH states is derived using several different methods. The propagators of the electrons and the quasiparticles are calculated for the above FQH states. The microscopic theory of the edge excitations for the Laughlin states is also presented. Some simple applications of the edge theory to the transport properties of the FQH states are discussed. In particular, the tunneling between edge states is shown to be a powerful tool to probe the internal topological orders in the FQH states. It can be used to distinguish different FQH states with the same filling fraction and to detect the non-abelian FQH states in experiments.

We investigate the statistical mechanics of a gas of fractional statistics particles in 2+1 dimensions. In the case of statistics very close to Fermi statistics (statistical parameter θ=π(1−1/n), for large n), the effect of the statistics is a weak attraction. Building upon earlier RPA calculation of Fetter, Hanna, and Laughlin for the case n=2, we argue that for large n perturbation theory is reliable and exhibits superfluidity (or superconductivity after coupling to electromagnetism). We attempt to describe the order parameter for this superconducting phase in terms of “spontaneous breaking of commutativity of translations” as opposed to the usual pairing order parameters. The vortices of the superconducting anyon gas are charged, and superconducting order parameters of the usual type vanish. We investigate the characteristic P and T violating phenomenology.

We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

Controllable magnetorheological (MR) fluid devices have reached the stage where they are in commercial production. Such devices are finding application in a variety of real world situations ranging from active vibration control to aerobic exercise equipment. Examples of several, commercial MR fluid devices are described and the comparative ability of MR and ER fluids to meet the needs of practical devices is discussed.

The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems. It gives a new interpretation of the concept of constant expansion in the homotopy perturbation method.

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with nonzero Chern number, C. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with nontrivial topology, C≠0, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with |C|>1. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.

This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references.

Numerical and analytical models of magnetorheological fluid phenomena that account explicitly for the effects of magnetic nonlinearity and saturation are described. Finite-element analysis was used to calculate the field distribution in chains of magnetizable particles. The field-dependent stress required to shear the chains was then obtained using the Maxwell stress tensor. Three regimes are identified: at low applied fields, the stress increase quadratically, as expected from linear magnetostatics. In intermediate fields, the contact or polar regions of each particle saturate, reducing the rate of increase of the stress with increasing field. At high fields, the particles saturate completely, and the stress reaches its limiting value. Approximate analytical expressions for the yield stress and shear modulus in these regimes are also derived. The predictions of these models are compared to magnetorheological experiments in the literature and from our laboratory. These models predict successfully the magnitude of the stresses as well as their field dependence. They also suggest that particles comprised of materials with higher saturation magnetizations will exhibit the largest magnetorheological effects.

A series of La 0.65 Ca 0.35-x Gd x MnO 3 (x = 0.00, 0.05, 0.15) samples were synthesized via a two-step route combining conventional solid-state reaction and high-pressure heat treatment. The effects of high-pressure processing and Gd 3+ substitution on the magnetocaloric properties and critical behavior of the phase transition were systematically investigated. X-ray diffraction analysis confirmed that all samples crystallize as a single-phase orthorhombic structure with the space group Pbnm. With increasing Gd 3+ content, the Curie temperature (T C ) gradually decreased to 132 K. Under an applied magnetic field of 7 T, the maximum magnetic entropy change (∣–ΔS M max ∣) decreased from 5.74 J·kg -1 ·K -1 (x = 0) to 3.89 J·kg -1 ·K -1 (x = 0.15). Despite the reduction in entropy change, the full width at half maximum of the magnetic refrigeration temperature span (ΔT FWHM ) broadened significantly from 70.76 K (x = 0) to 100.14 K (x = 0.15), corresponding to an enhancement of 41.5%. The nature of the magnetic phase transition was determined using Arrott plots, universal scaling curves, and the field exponent. The results reveal that the x = 0.00 and x = 0.05 samples undergo first-order magnetic transitions, whereas the x = 0.15 sample exhibits a second-order transition. Critical behavior analysis further demonstrates that the phase transition of the x = 0.15 sample can be well described by the mean-field model, yielding a critical exponent β = 0.485. Compared with literature data for samples synthesized under ambient pressure, high-pressure heat treatment effectively enhanced the T C of samples with identical compositions, providing a promising synthetic strategy for designing low-temperature magnetocaloric materials with broadened operating temperature windows.

Modulated compressional dispersive Alfvén waves find diverse applications within the field of plasma physics. Alfvén waves are a form of plasma waves in which ions oscillate under the influence of a restoring force generated by the tension in the magnetic field lines. This manuscript aims to apply a specific integration scheme to generate various optical solitons for the presented model, thereby minimizing experimental time and costs. In this article, the nonlinear Schrödinger equation, which depicts the dynamics of the modulated compressional dispersive Alfvén envelope model in (1+1)-dimensions, is explored, and new closed-form solutions are investigated. An appropriate wave transformation is utilized to turn the governing equation into an ordinary differential equation. The extended sinh-Gordon equation expansion and modified auxiliary equation procedures are implemented on the investigated model to get optical solitons and other solitary wave solutions. By using the execution of these techniques, rational, trigonometric, and hyperbolic function solutions are obtained. Stability analysis via modulation instability is also carried out in the paper. The physical interpretation of these closed-form solutions have been analyzed by constructing the graphical representations. Some selected solutions are depicted through two- and three-dimensional graphs to demonstrate the behavior of these solutions. The graphs present dark soliton, bright soliton, and periodic wave solutions. The acquired results are novel and confirm that the proposed techniques are reliable, efficient, and useful tools for addressing complex phenomena in engineering, mathematical physics, and optical fiber.

Using a three-dimensional classical ensemble model, we theoretically investigate the intensity dependence of nonsequential double ionization (NSDI) of argon atoms driven by a spatially inhomogeneous laser field. The numerical results show that the correlated electron momentum distribution (CEMD) is highly sensitive to the laser intensity, with the most pronounced changes appearing in the low- and high-momentum regions. In the high-momentum region, the relative contribution of electron pairs to NSDI first increases and then tends to stabilize with increasing laser intensity, while the distribution remains concentrated near the diagonal. In contrast, in the low-momentum region, the initially focused diagonal distribution gradually broadens and evolves into a pronounced arc-like structure at high intensity. Back analysis reveals that the dominant recollisionimpact ionization (RII) events can be classified into four typical trajectory classes. Electron pairs originating from different trajectory classes populate different regions of the CEMD and exhibit distinct momentum-correlation patterns. The intensity-dependent relative weights of these trajectory classes are responsible for the observed evolution of the CEMDs. These results provide a clear physical picture for controlling correlated electron dynamics in spatially inhomogeneous laser fields.

Multifunctional nanocomposites with tuneable properties have attracted attention for environmental and biomedical applications. Ce incorporation can modify their structural, optical, thermal and functional properties. In this work, PVP (polyvinylpyrrolidone) capped Ce-doped CuO/Mg(OH) 2 nanocomposites were successfully synthesised using co-precipitation method. Three synthesised samples are identified in manuscript by the sample codes NC1, NC2, and NC3: undoped CuO/Mg(OH) 2 , 2 mol% Ce-doped CuO/Mg(OH) 2 , and 4 mol% Ce-doped CuO/Mg(OH) 2 , respectively. All samples were explored with various analytical characterisation techniques to study the influence of Ce incorporation on multifunctional properties of the nanocomposites. XRD confirmed the polycrystalline nature of nanocomposites, consisting monoclinic CuO and hexagonal Mg(OH) 2 phases, with a slight decrease in crystallite size upon Ce incorporation. HRTEM and FESEM analyses revealed the nearly spherical and sheets like morphologies, while EDS spectra and elemental mapping confirmed the presence and distribution of Cu, Mg, O and Ce. FT-IR analysis identified various functional groups present in nanocomposites, whereas XPS confirmed the oxidation states of Cu 2+ , Mg 2+ , and Ce 3+ /Ce 4+ . TGA-DSC analysis revealed weight loss and thermal decomposition behaviour of the nanocomposites. UV-visible DRS analysis exhibited low reflectance below 700 nm and a reduction in optical bandgap energy with increasing Ce concentration. The 4 mol% Ce-doped CuO/Mg(OH) 2 nanocomposite exhibited 95.67% degradation of methyl orange and 98.11% of methylene blue within 120 and 60 min, respectively, under UV-visible irradiation. The same sample achieved 90.43% DPPH free radical scavenging activity. The antibacterial assays of 4 mol% Ce-doped CuO/Mg(OH) 2 nanocomposites exhibited zone of inhibition (ZOI) of 29.33 ± 0.57 mm, and 32.66 ± 0.47 mm, against bacteria strain Escherichia coli (E. coli), and Bacillus subtilis (B. subtilis), respectively. Thus, the synthesised Ce-doped CuO/Mg(OH) 2 nanocomposites represent a new class of multifunctional materials with potential applications in photocatalysis, antioxidant and antibacterial activity.

Lead-free perovskites have attracted increasing attention as environmentally friendly absorber materials for next-generation solar cells. In this work, a bilayer perovskite solar cell based on Cs 2 TiBr 6 and Cs 2 SnI 6 was designed and simulated using SCAPS-1D, with the structure FTO/ETL/Cs 2 TiBr 6 /Cs 2 SnI 6 /HTL/Au. The Cs 2 TiBr 6 /Cs 2 SnI 6 bilayer configuration not only mitigates lead toxicity but also enhances device stability and light-harvesting capability. The effects of various hole transport layers (HTLs) and electron transport layers (ETLs) were systematically analyzed, highlighting that optimal energy-level alignment between absorber and transport layers is crucial for efficient carrier separation and transport. Furthermore, the influence of absorber thickness, doping concentration, defect density, and back electrode work function on device performance was investigated. Under optimized conditions, the bilayer device achieved a short-circuit current density of 26.72 mA/cm 2 , an open-circuit voltage of 1.43 V, a fill factor of 85.05%, and a maximum power conversion efficiency of 32.51%. These results demonstrate the great potential of Cs 2 TiBr 6 /Cs 2 SnI 6 bilayer perovskites for high-efficiency, lead-free photovoltaic and optoelectronic applications.

This work proposes a dual-layer ultra-thin polarization-insensitive metamaterial for ultra-wideband microwave absorption. The proposed metamaterial absorber (MMA) consists of two resistive frequency selective surfaces (RFSS) constructed in a grounded dielectric substrate. The two RFSSs, although with the same unit cell periodicity, have different geometric patterns and significantly different surface impedances, resulting in distinct reflection, transmission and absorption properties. The independent electromagnetic simulations of the two RFSSs provide their reflection and transmission coefficients. Leveraging these simulation results, a detailed theoretical analysis based on interference theory predicts that the MMA can achieve ultra-wideband absorption. Numerical simulations demonstrate that the MMA achieves over 90% absorption from 4.3 to 31.3 GHz under normal incidence of arbitrarily polarized waves. Its total thickness is merely 5.3 mm, thus yielding a high bandwidth-to-thickness ratio (BTR) of 11.35. Moreover, the MMA exhibits good angular stability, for incident angle up to 60°, its absorptivity under TM wave incidence remains above 97% across the frequency band of 8.7-33.7 GHz. Finally, experimental measurements on a fabricated sample further validate the absorption performance of the MMA. Overall, the proposed MMA can achieve ultra-wideband absorption and has a higher BTR compared to numerous previous designs, making it highly attractive in practical applications.

Superinsulation is the confining phase of condensed matter systems. It is a genuine quantum state of matter, dual to superconductivity, just as confinement in particle physics is dual to the Higgs phase. In contrast to hadron physics, the gauge field that becomes confining is not colour SU(3) but the conventional U(1) electromagnetic field. Superinsulation arises in superconductors with an emergent granular condensate when core-less XY vortices between condensate grains become tensionless, unobservable Dirac strings and magnetic monopoles are liberated and condense. This magnetic condensate confines electric fields into flux tubes, strings that generate a linear potential between Cooper pairs. These dual Abrikosov flux tubes give rise to infinite electrical resistance, persisting up to a finite deconfinement temperature. We shall review the theoretical framework of superinsulation together with its experimental validation, including the direct observation of the linear confining potential and we shall stress how phase-only approaches and disorder-based ideas for the phases around the superconductor-to-insulator transition are hard to reconcile with recent experimental observations.

In this paper, we study a time-dependent variable-coefficient form of the Boiti–Leon–Manna–Pempinelli equation, which models nonlinear waves in nonuniform media. The Painlevé analysis shows that the proposed equation possesses the Painlevé property under the stated local nondegeneracy assumptions, thereby providing strong evidence for an underlying integrable structure rather than, by itself, a complete proof of integrability. By applying the Hirota bilinear method together with the KP hierarchy reduction, we construct exact multi-soliton and breather-type solutions and derive rational-degenerate and semi-rational limits from the same Gram determinant. The breather reduction is obtained from complex-conjugate spectral pairs and the same spectral constraint as the soliton determinant. The corrected long-wave degeneration produces meromorphic rational and semi-rational solutions whose tau functions may vanish, so they are not claimed to be globally nonsingular lumps or rogue waves. Based on our literature survey, the KP hierarchy reduction has not previously been applied to this time-dependent variable-coefficient form of the BLMP equation. The results reveal non-autonomous kink motion, oscillatory breather dynamics, and algebraically localized meromorphic degenerations. In the constant-coefficient limit, the construction also yields corresponding exact solutions of the classical Boiti–Leon–Manna–Pempinelli equation. These findings extend the model and offer useful insight into nonlinear wave behavior in realistic physical systems.

In this manuscript, we investigate the optical hydromagnetic recursive visco-magnetic Belavin-Polyakov model for thermal Heisenberg radiation in de Sitter Heisenberg space. We define the conformal magnetical Heisenberg microfluidics magnetic [Formula: see text]microbeam and establish the vissco radiation Heisenberg solidity. The recursive magnetical Heisenberg microfluidics conformal Heisenberg microbeam magnetic field is constructed, followed by the optical Belavin-Polyakov visco-magnetic phase for heat visco-recursive microfluidics conformal Heisenberg thermal radiation. Finally, we present the optical Heisenberg thermal visco-magnetic Belavin-Polyakov conducting of the conformal Heisenberg microbeam. Optical physical model of [Formula: see text]microbeam solidity, visco-magnetic phase, and thermal radiation are explicitly formulated.

Nanocrystalline B2 CuZr alloys are of significant interest due to their mechanical relevance in shape memory systems and metallic glass composites, where grain-scale deformation mechanisms critically influence macroscopic response. In this work, molecular dynamics simulations are combined with machine learning structural classification to investigate the tensile deformation behavior of nanocrystalline B2 CuZr with varying grain sizes. Uniaxial tensile tests reveal a clear grain-size dependence of the ultimate tensile stress, with larger average grain sizes exhibiting higher peak strength, while the flow stress shows a weaker sensitivity to grain size. Atomic scale analysis demonstrates that plastic deformation is dominated by grain boundary mediated mechanisms, including atomic rearrangements, atomic migration from grains to grain boundaries, progressive grain shrinkage, and void nucleation, rather than stress-induced martensitic transformation commonly observed in single-crystal B2 CuZr. Overall, the machine learning classifiers used here enabled the identification of distorted B2 environments, grain boundaries, defect structures, and void surfaces during deformation, providing a comprehensive description of the microstructure evolution. These results provide a general data-driven framework for analyzing complex deformation processes in crystalline materials.