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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editors-in-Chief: Gernot Alber and Jürgen Schnack
Edited by: Silvia De Bianchi , Hans-Thomas Elze , Claus Kiefer and Klaus Morawetz

Language: English

First published: February 20, 1946

Publication Frequency: 12 issues per year

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About this journal

Objective
A Journal of Physical Sciences: Zeitschrift für Naturforschung A (ZNA) is an international scientific journal which publishes original research papers from all areas of experimental and theoretical physics. Authors are encouraged to pay particular attention to a clear exposition of their respective subject, addressing a wide readership. In accordance with the name of our journal, which means “Journal for Natural Sciences”, manuscripts submitted to ZNA should have a tangible connection to actual physical phenomena. In particular, we welcome experiment-oriented contributions.

Manuscripts considered for publication in A Journal of Physical Sciences: Zeitschrift für Naturforschung A undergo high-level refereeing. Mere formal correctness of a paper is not sufficient for its acceptance. Moreover, articles reporting a merely marginal extension of already existing knowledge are considered unsatisfactory. Instead, the key quality a publication in A Journal of Physical Sciences: Zeitschrift für Naturforschung A should possess is that it makes a genuine contribution to the advancement of its topic.

Topics

Atomic, Molecular & Optical Physics
Chemical Physics
Dynamical Systems & Nonlinear Phenomena
Fundamental Concepts of Physical Sciences
Gravitation & Cosmology
Hydrodynamics & Plasma Physics
Nuclear Physics & Particle Physics
Quantum Field Theory
Solid State Physics & Materials Science
Thermodynamics & Statistical Physics

Article formats
Original research articles, research notes, letters and review articles from all areas of theoretical and experimental physics

Information on submission process

Editors’ Choice

Zeitschrift für Naturforschung A – A Journal of Physical Sciences is proud to announce a new feature, the Editor’s Choice free access article. To download the featured article free of charge, please click the link below.

Vol. 76, Iss. 12: Spin coherent states, Bell states, spin Hamilton operators, entanglement, Husimi distribution, uncertainty relation and Bell inequality by Dylan Durieux and Willi-Hans Steeb

Vol. 76, Iss. 12: Mathieu-state reordering in periodic thermodynamics by Onno R. Diermann

Vol. 76, Iss. 11: Exact Beltrami flows in a spherical shell by Oleg Bogoyavlenskij

Vol. 76, Iss. 9: Accuracy of the typicality approach using Chebyshev polynomials by Henrik Schlüter, Florian Gayk, Heinz-Jürgen Schmidt, Andreas Honecker and Jürgen Schnack

Vol. 76, Iss. 8: Stochastic thermodynamics of a finite quantum system coupled to a heat bath by Heinz-Jürgen Schmidt, Jürgen Schnack and Jochen Gemmer

Vol. 76, Iss. 3: Interaction of waves in one-dimensional dusty gas flow by Pooja Gupta, Rahul Kumar Chaturvedi and L. P. Singh

Vol. 75, Iss. 7: Admissibility conditions for Riemann data in shallow water theory by Martin O. Paulsen and Henrik Kalisch

Vol. 75, Iss. 5: Special Issue: Physics of Non-Equilibrium Systems/ Issue Editors: Martin Holthaus and Andreas Engel

Vol. 75, Iss. 2: Quantum-Phase-Field: From de Broglie-Bohm Double-Solution Program to Doublon Networks by J. Kundin and I. Steinbach

Vol. 74, Iss. 8: Special Issue: Trends an Perspectives in Engery Research/ Issue Editors: Martin Holthaus and Sascha Schäfer

Vol. 72, Iss. 2: Special Issue: Heat Transfer and Heat Conduction on the Nanoscale / Guest Editors: Svend-Age Biehs, Philippe Ben-Abdallah, Achim Kittel

Vol. 71, Iss. 10: Focus Section: Emergence in Driven Solid-State and Cold-Atom Systems / Guest Editors: Ludwig Mathey, Junichi Okamoto

History

The "Zeitschrift für Naturforschung A - A Journal of Physical Sciences" (ZNA) is an international scientific journal that publishes original research papers from all areas of experimental and theoretical physics. The journal has had a tradition of excellence since its first issue in early 1946.

History of ZNA: A Modern Journal with Tradition

Free access to virtual issue: seminal papers of eminent physicist published throughout the journal’s history

The "Zeitschrift für Naturforschung" – translated literally: Journal for Research in Natural Sciences – was founded by Alfred Klemm together with Hans Friedrich-Freksa in 1945, providing a badly needed functioning means of professional communication for scientists in postwar Germany.

In this tradition, ZNA is serving the international scientific community still today as an efficient, up-to-date communication platform which covers all areas of experimental and theoretical physics, combining rigorous publication standards with high visibility.

Please have a look at the comprehensive history of ZNA in the document "About this Journal".

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A novel machine learning framework to approximate modified Bessel functions

August 20, 2025

Anuwedita Singh

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This article presents the precise approximations for modified Bessel functions of the second kind. Building on a well-established method for function approximation, the enhanced approach, incorporating machine learning techniques, is used to approximate Bessel functions such as K 0 , K 1 , K 1/4 , I 0 , I 1 , and I 1/3 . These approximations are demonstrated to be highly effective in various applications, such as thermal average and partition function, providing a robust alternative to repeated numerical integration.
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Elastic softening and lattice dynamical insights into thermoelectric CdS_1−xSe_x alloys

August 15, 2025

Avinash Chandra Rai, Alok Kumar Verma, Vivek Kumar Srivastava, Garima Vaish

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Ternary alloys of group II–VI semiconductor are trending due to their tunable optical, electronic and thermoelectric properties. This work includes the evaluation of mechanical, thermophysical and ultrasonic behaviour of ternary alloys CdS 1− x Se x at room temperature. This analysis presents linear and nonlinear behaviour of the elastic constants of Cadmium-sulfo-selenide alloys for their different compositions using many-body Lennard-Jones potential interaction model. The mechanical and thermo-physical properties of CdS 1− x Se x have been evaluated using the second and third order elastic constants. Behaviour of propagation of ultrasonic waves in these alloys has been examined for non-destructive evaluation. For this, we have determined the longitudinal, shear, quasi-shear components of ultrasonic velocities and Debye average velocity in different crystallographic directions. Substituting Se in CdS enhances its thermoelectric potential by offering mechanical flexibility and improved anharmonic stability, reducing lattice thermal conductivity. This theoretical insight highlights CdS 1− x Se x as a promising system for doping strategies and future experimental exploration in next-generation thermoelectric materials.
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Artificial neural network solution of Maxwell hybrid nanofluid with multiple slips, with radiation effects flowing across a porous extending sheet

August 12, 2025

Zeeshan, Waris Khan, Imed Boukhris, Mohamed Kallel, Hakim AL Garalleh

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Heat transfer phenomena in non-Newtonian nanofluids (N-N-Fs) are extensively observed across various disciplines, including nautical science, fluid biology, melt-spinning, thermal control over metallic material, protecting systems for thermal exchangers, and delays. In light of the aforementioned significance, the present investigation centers on the implementation of an artificial neural network (ANN) model to analyze the behavior of magneto-hybrid Maxwell nanofluid (MHMNF-ANN) flow across a stretched surface in a permeable medium, highlighting the novel application of hybrid nanofluid, taking into account the effects of heat generation/absorption, different slip situations, and solar radiation. The research holds significant implications for various domains such as magnetohydrodynamics (MHD) mechanisms, thermal exchange systems, and porous media, in addition to advancements in nanofluid technology. Hybrid nanoparticles composed of alumina and magnetite are suspended within a 50:50 aqueous solution of water and ethylene glycol (WEG) to constitute the hybrid nanofluid. The numerical solution is derived through the application of the RK45 method utilizing MATLAB software. The acquired dataset was employed to train the artificial neural network (ANN) model, which was subsequently validated against numerical values of significant engineering parameters. Effect of emerging factors on the flow dynamics is reported through graphs and tables.
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Examining the influence of molar ratio variation over the phase variance observed in hydrogen bond liquid crystal binary mixtures formed between benzoic acids and 4-Nitrobenzaldehyde

August 8, 2025

Ravichandran Balaji, Nataraj Pongali Sathya Prabu

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Four binary mixtures are isolated from two hydrogen bond mesogenic complexes that are formed between p-n alkyloxy benzoic acids and 4-Nitrobenzaldehyde. The carbon chain length chosen for the formation of binary mixtures are heptyloxy and octyloxy benzoic acids. 4-Nitrobenzaldehyde (NBA) and heptyloxy benzoic acid mesogenic complex is treated as X component while 4-Nitrobenzaldehyde (NBA) and octyloxy benzoic acid mesogenic complex is treated as Y component. Binary mixtures are obtained by varying the molar ratio of the two mesogenic complexes ( X and Y ) in even steps viz., from 0.2 to 0.8. Hydrogen bond existence between the binary mixtures is confirmed through Fourier Transform Infrared Spectroscopy. Mesogenic phase variance is investigated through polarizing optical microscope study. The phase transition temperature and their corresponding enthalpy values are analyzed via differential scanning calorimetry. Thermal equilibrium, thermal stability, order of phase transition and specific heat capacity of the binary mixtures are also elucidated from the thermograms of the mesogenic mixtures. The results obtained make these binary mixtures a potential candidate for opto-electronic and thermal energy based applications.
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Heat transfer study of solidification of eutectic alloys with temperature-dependent solid fraction and time-dependent heat flux

July 29, 2025

Sunil Kumar Sharma

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Although the solidification behavior of eutectic alloys has been widely studied, the growth rate of solid fraction as a function of local temperature remains less explored. A theoretical model of the three-region solidification process is proposed that includes the linear relationship between the solid fraction and the temperature of the mushy zone. A physically realistic, time-dependent heat transfer is considered a driving function of the solidification process. The analytical solution of the proposed model is determined by converting the given partial differential equations into ordinary differential equations by using the similarity transformation. The detailed discussion of the model is presented by taking the thermal–physical properties of Al–Cu composition with 5 % Cu. The validity of the current model is shown with the previous model and found that the current model offers a faster solidification rate with the least energy consumption and thus minimizes the operating time. It is found that material solidifies slower after formation of the mush form due to thermal resistance. Due to the greater value of heat transfer constant Ω, greater heat is removed from the surface of the liquid alloy and material gets solidified faster. The observations found in this study may be relevant for solid solutions and eutectic alloys.
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Preparation, properties, and application of titanium carbide coatings

July 25, 2025

Daniela Nedeva

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This study aims to investigate the structural, mechanical, and tribological properties of titanium carbide coatings, focusing on the influence of deposition techniques, including chemical vapor deposition and physical vapor deposition, on their phase composition, morphology, and adhesion. The research combines experimental characterization and numerical modeling to analyze grain structure, hardness, adhesion strength, and thermal stability. The findings reveal that coatings obtained through chemical vapor deposition exhibit superior crystallinity with a hardness of 2,500 Vickers hardness and a critical adhesion load exceeding 80 N, alongside a denser microstructure. In contrast, coatings produced by physical vapor deposition present finer grains and improved surface smoothness, making them particularly advantageous for tribological applications. Thermal expansion modeling has been performed to assess the role of deposition techniques in stress development, identifying potential failure points when exposed to high temperatures. Furthermore, the study explores titanium carbide–hydroxyapatite composites, demonstrating their enhanced wear resistance, bioactivity, and nontoxic characteristics, which make them promising candidates for biomedical applications. The results significantly contribute to the optimization of deposition strategies, improving the mechanical performance and extending the range of potential applications of titanium carbide coatings. These applications include cutting tools, aerospace components, high-temperature protective coatings, and medical implants. The insights gained from this research offer valuable guidance for advancing the development of titanium carbide-based materials and enhancing their practical utility in modern engineering and biomedical fields.
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Investigation of (n, γ) rates of ^79,81Br and ^85,87Rb in the s-process nucleosynthesis

July 25, 2025

Zain Ul Abideen, Abdul Kabir, Kaif Nabi, Muhammad Ali Mushtaq, Noor-Ul Amin, Sadiq Usman

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We report a systematic investigation of neutron capture reactions on 79,81 Br and 85,87 Rb under conditions characteristic of the weak s -process in massive stars. Employing the Hauser–Feshbach frameworks in TALYS v1.97 and YAHFC v3.66, we explore a broad suite of nuclear level density and γ strength models, both phenomenological and microscopic, to assess their influence on Maxwellian-averaged cross sections. By benchmarking our predictions against available experimental data, we identify model combinations that consistently reproduce observed trends, thereby greatly reducing uncertainties in the cross sections. The results provide experimentally validated reaction rates that can strengthen the reliability of s -process nucleosynthesis simulations.
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QSPR modeling of physicochemical properties in atmospheric photo-oxidized indole derivatives: integrating topological indices with linear, quadratic, and logarithmic regression

July 21, 2025

Huang Wei, Shamaila Yousaf, Fiza Bibi, Sobhy M. Ibrahim, Adnan Aslam

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This study bridges graph-theoretical methods and computational physics by evaluating degree-based topological indices for sixteen indole derivatives-indole, 2-Formylformanilide, indoxyl, isatin, anthranilic acid, isatoic anhydride, indigo dye, indirubin, tryptanthrin, indoxyl red, 1H-indole-4-amine, 2-methyl-1H-Indole, 2-phynel-1H-indole, 1H-indole-6-carbaldehydel, 1h-indole-3-carbaldehyde, and 5-chloro-1h-indole to predict their physicochemical properties. By interpreting molecular structures as quantum-mechanical graphs, we compute topological indices as descriptors of electronic and structural connectivity, which are then employed in linear, quadratic, and logarithmic regression models to estimate density, boiling point, melting point, water solubility, molecular weight, and vapor pressure. These properties are critical for understanding molecular interactions, phase transitions, and material behavior in condensed matter systems. Statistical evaluation ( r , r 2 , F-statistic, p -value) reveals robust predictive accuracy for boiling point ( r > 0.824) and molecular weight ( r > 0.99), aligning with their direct dependence on molecular topology and quantum mechanical parameters. The models for vapor pressure and solubility also demonstrate moderate success, reflecting their sensitivity to intermolecular forces and entropy-driven processes. By linking graph invariants to measurable physical properties, this work advances computational strategies for rapid material characterization, offering a scalable alternative to resource-intensive quantum simulations. The results highlight the potential of topological indices as low-cost, high-efficiency tools for designing organic semiconductors, photonic materials, and molecular sensors, with implications for condensed matter physics and nanotechnology. This approach underscores the synergy between discrete mathematics and physical chemistry, enabling predictive modeling of complex systems through a unified theoretical framework.
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Hopf-induced desynchronization

July 9, 2025

Seungjae Lee, Lennart J. Kuklinski, Moritz Thümler, Marc Timme

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The emergence of synchrony essentially underlies the functionality of many systems across physics, biology and engineering. In all established synchronization phase transitions so far, a stable synchronous state is connected to a stable incoherent state: For continuous transitions, stable synchrony directly connects to stable incoherence at a critical point, whereas for discontinuous transitions, stable synchrony is connected to stable incoherence via an additional unstable branch. Here we present a novel type of transition between synchrony and incoherence where the synchronous state does not connect to the state of incoherence. We uncover such transitions in the complexified Kuramoto model with their variables and coupling strength parameter analytically continued. Deriving a self-consistency equation for a quaternion order parameter that we propose helps to mathematically pin down the mechanisms underlying this transition type. Local numerical analysis suggests that the transition is linked to a Hopf bifurcation destabilizing synchrony, in contrast to branching point bifurcations established for the transition between synchrony and incoherence so far.
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Thermal vibration of butterfly auxetic metamaterial core sandwich nanoplate with piezoelectric surface layers

July 7, 2025

Adem Fatih Ozalp

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The thermal vibration behavior of a butterfly auxetic core sandwich nanoplate with Piezoelectric surface layers is the main subject of this study. Used model employs the Nonlocal Strain Gradient Theory (NSGT) and Higher-Order Shear Deformation Theory (HSDT). The research systematically examines the combined effects of thermal loading, auxetic core geometry, and piezoelectric properties on the dynamic response of the nanoplate. Through numerical analysis, the influence of key parameters, including auxetic core dimensions, temperature rise, electric field, and plate thickness on the non-dimensional frequency and buckling characteristics is evaluated. The results reveal that auxetic structures significantly modify vibrational behavior, with increased auxeticity (negative Poisson’s ratio) leading to reduced stiffness under thermal loading. Furthermore, the study highlights the critical role of boundary conditions, demonstrating that clamped edges exhibit greater rigidity compared to simply supported configurations. These findings provide information for the design and optimization of sandwich structures, particularly in applications where thermal and mechanical loads are prevalent, such as microelectromechanical systems, aerospace, and other advanced engineering systems.
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Towards relativistic type-II superconductivity: a scalar electrodynamics approach

July 3, 2025

Stanley A. Bruce

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This work advances our 2D scalar electrodynamics (SED) model, a relativistic analogue of type-II superconductivity, by implementing a cylindrical coordinate representation. This adaptation addresses the importance of cylindrical symmetry in describing 2D systems, especially those featuring Dirac fermion bound states in magnetic fields. Focusing on a specific example, we explore the relativistic limit, significant in astrophysical environments like neutron-star cores, where magnetic fields reach critical levels. Along the lines of the Ginzburg–Landau theory we postulate the structure the proton vortex-supercurrent, and connect it with the SED current. From this connection we analytically determine the squared modulus of the relativistic order parameter state which is to be proportional to the local density of Cooper pairs in the superconducting condensate. This study could contribute to the theoretical understanding of superconductivity in strong electromagnetic fields within the SED framework, with potential applications to neutron star physics.
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Finite-dimensional Lie superalgebra spo(2N, 2) and osp(2N, 2) and their applications

June 24, 2025

Linlin Gui, Yufeng Zhang, Haifeng Wang

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A new type of high-dimensional Lie superalgebras is constructed, including Lie superalgebras spo(4, 2) and osp(4, 2). Based on it, two different coupled nonisospectral super AKNS hierarchies and their bi-Hamiltonian structures are obtained. Then, the Lie superalgebras spo(4, 2) and osp(4, 2) are expanded to infinite-dimensional Lie superalgebras spo(2N, 2) and osp(2N, 2). It follows that we present the generation of multi-component super integrable hierarchy, and deduce two different multi-component super integrable AKNS hierarchies and their Hamiltonian structures.
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Degree-based topological indices and total π-electron energies of some benzenoid hydrocarbons: correlations of strain energies and bulk modulus with such indices

June 17, 2025

Swapnadeep Mondal, Bholanath Mandal

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Degree-based and neighbourhood degree-sum-based (or hybrid degree-based) topological indices (TIs) for some benzenoid hydrocarbons viz. linear polyacences, methylene substituated linear polyacences, cyclacenes, linear poly ( p -phenylenes), methylene substituated linear poly ( p -phenylenes), and cylindrical poly ( p -phenylenes) with r hexagonal rings are expressed as linear functions of r . For a given system the variation of degree-based Randić and harmonic indices or that of their hybrid indices with r is quite similar while that differs with their corresponding hybrid degree-based indices. The geometric-arithmetic index is the only one among the indices for a given system which is found to remain unaffected under consideration of neighbourhood effect. Total π -electron energies for such systems have also been derived as linear functions of r from their respective eigenspectra. Although all such TIs discussed here have good linear correlations with the total π -electron energies of the respective systems but among them the geometric-arithmetic degree-based and hybrid degree-based TIs are the best to correlate total π -electron energies for such systems. The inverses of the degree-based and hybrid degree-based TIs of cyclacenes and cylindrical poly ( p -phenylenes) are found to correlate excellently well with their strain energies. The good linear correlations are also found with the inverses of the TIs of linear poly ( p -phenylenes) with 2–6 hexagonal rings and their respective bulk modulus.
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Semi-empirical cross-sections and astrophysical S-factor values of ⁷Be(p, γ)⁸B reaction in the low energy range

June 16, 2025

Ercan Yildiz

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The reaction 7 Be(p,γ) 8 B plays a significant role in the evaluation of solar neutrino fluxes. Therefore, this reaction has a significant place in the proton-proton chain. Particularly at low energies, the reaction cross-sections and astrophysical S-factor values play a crucial role to explain its effects in the proton-proton chain. TALYS 1.95 nuclear reaction code were used to calculate theoretical cross-sections which are used to obtain both theoretical astrophysical s-factors and semi-empirical formula. In this way, more suitable estimates are made for the low energy range. The obtained results were analyzed in comparison with experimental data extracted from the EXFOR nuclear database.
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Semi-analytical solution of dissipative rogue waves and breathers in nonthermal plasma

May 26, 2025

Eman I. El-Awady

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This work examines the propagation of dissipative dust-ion-acoustic (DIA) waves in a plasma with non-thermal electrons, heated positive ions, and stationary negative dust particles. This discussion also includes dissipative rogue waves (DRWs) and breathers. The linear damped nonlinear Schrödinger equation (dNLSE) and its detailed derivation are described here. When it comes to differential equations, the dNLSE is believed to be one that cannot be integrated. As a result of this, even with the inclusion of the linear damping term, there is still no solution that is accurate. In light of this, we will proceed to meticulously derive and present the semi-analytical solution today. This method allows for the analytical solution of the fundamental nonlinear Schrödinger equation (NLSE), with the damping term being left out of the equation. Using this method as a starting point, one can begin the process of solving the linearly damped NLSE. In addition to this, we will evaluate the analytical solutions of the standard NLSE in comparison to the approximate analytical solutions of the dNLSE. The manner in which plasma properties influence the characteristics of dissipatively modulated DIA waves is the subject of extensive research. To be more specific, the nonthermal electron count, the kinematic viscosity of the ions, and the temperature ratio of the ions to electrons are all taken into consideration. There is a possibility that this work will shed light on the modulated DIA structures that are present in both laboratory plasmas and space plasmas, as well as make predictions regarding such structures.

Journal Impact Factor	1.3	2024, Journal Citation Reports (Clarivate, 2025)
5-year Journal Impact Factor	1.2	2024, Journal Citation Reports (Clarivate, 2025)
Journal Citation Indicator	0.33	2024, Journal Citation Reports (Clarivate, 2025)
CiteScore	3.0	2024, Scopus (Elsevier B.V., 2025)
SCImago Journal Rank	0.253	2024, SJR (Scimago Lab, 2025; Data Source: Scopus)
Source Normalized Impact per Paper	0.511	2024, CWTS Journal Indicators (CWTS B.V., 2025; Data Source: Scopus)

Zeitschrift für Naturforschung A

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