Orbital Structure Research Articles

Optimization of Mechanical Properties during Cold Rolling and Wrap-Forming for Metal Helical Tubes

The proposed method involves the utilization of a strip roll-forming technique to fulfill the specific requirements for constructing large-scale structures in orbit and space station trusses during extraterrestrial exploration. This involves progressively rolling out a metal strip with an L+V-shaped locking edge through multiple passes of forming rolls featuring different section shapes. The process of helical locking enables the formation of a slender, spiral-shaped tube, which can be utilized for the in-orbit assembly of exceptionally large structures. The proposed approach introduces a two-step optimization method to enhance the maximum stress, equivalent plastic strain, and wrapping torque of roll-forming L+V cross-sections and wrap-forming helical tubes. The optimized sample points in the second step are established based on the optimal roll distance and roll gap obtained in the first optimal step, resulting in the determination of the optimal folding height and V-shaped angle of the L+V strip cross-section after optimization. The design of the strip wrapping configuration that follows is highly dependent on these four parameters.

Anatomical structure of the orbits of the European beaver (Castor fiber)

Understanding the specifics of the orbit of each species is a fundamental and crucial step in developing veterinary ophthalmology. This article describes the bone structure, foramina piercing the bones, and the shape of the orbit in the European beaver (Castor fiber). Additionally, a morphometric analysis of the orbit was conducted, measuring its height, width, and depth, and the orbital index was calculated. A total of 27 skulls of this species were used for the study. It was shown that the average length and depth of the orbit were greater in females, while the average width was comparable in both sexes. Males, however, had a higher average orbital index. The observed regularities, assessed with a T-test, showed statistically significant differences between individuals. These results are the first step towards developing reference values for the discussed dimensions for this species, which will allow for the assessment of the correctness of the orbit structure of the European beaver.

Evaluation of the Effect of Topical Prostaglandin Analog Treatment on Orbital Structures in Open-Angle Glaucoma with Computed Tomography

Background/Objectives: This study aims to evaluate the computed tomography (CT) scans of glaucoma patients using prostaglandin analogs (PGA) in one eye, investigate findings associated with prostaglandin-associated periorbitopathy (PAP), and compare these findings with those of the contralateral eyes. Methods: Patients with open-angle glaucoma who had CT images of the orbital region taken for another reason at least one month after starting PGA treatment in one eye were included in the study. Enophthalmos measurements from thin-slice CT images, along with 3D volume measurements of orbital fat tissue, periorbital muscles, and the optic nerve, were performed. Ophthalmological examination findings and treatment information were collected. The values were compared with those of the contralateral eyes of the same patients not using PGA. Intraclass correlation coefficients (ICCs) were computed to evaluate measurement repeatability. Results: Forty patients were included in the study. Among them, 29 (72.5%) used latanoprost, 9 (22.5%) used bimatoprost, and 2 (5%) used travoprost. The mean enophthalmos values on the treated side (15.5 ± 2.0 mm) were lower than on the untreated side (16.1 ± 1.4 mm), but this difference was not statistically significant (p = 0.07). In 29 patients (72.5%), enophthalmos measurements were smaller on the treated side, with 7 patients (17.5%) showing a difference of 2 mm or more. No significant correlation was found between the duration of PGA use and enophthalmos measurements (p = 0.768 r = −0.048). Additionally, no significant differences were found in orbital fat volume, total extraocular muscle volume, and optic nerve volume (p > 0.05). ICC values demonstrated excellent reliability (ICC > 0.75) for all measurements. Conclusions: We did not find significant differences in enophthalmos measurements, orbital fat volume, total muscle volume, and optic nerve volume between the PGA-treated and untreated eyes.

Vessel wall MRI in giant cell arteritis: standardized protocol and scoring approach developed by an international working group.

There are an increasing number of centers performing research on high-resolution vessel wall magnetic resonance imaging (VW-MRI) in giant cell arteritis (GCA). However, harmonized approaches to VW-MRI in GCA are lacking and are essential to performing multicentre studies. Using a data-driven, consensus-based approach, an international expert group developed a standardized MRI protocol and scoring system to advance multi-centered research in cranial GCA. A targeted literature review of VW-MRI in cranial GCA was conducted. A working group comprised of radiologists, rheumatologists, and ophthalmologists with expertise in VW-MRI and GCA reviewed the results of the literature search, presented relevant data and images from their respective centers, and then reached consensus on recommendations related to key MRI structures, MRI sequences, scoring system, and other important considerations. A total of 21 relevant articles were identified and reviewed. Based on published literature, structures to be evaluated on MRI were categorized based on anatomic location (extradural cranial, intradural cranial, and orbits) and prioritization (core vs elective). Essential and elective sequences to comprehensively image cranial and orbital structures while minimizing scan time were determined along with scoring systems to grade contrast enhancement. This report describes a standardized approach to facilitate research of VW-MRI in cranial GCA that is the result of a multi-disciplinary, international collaboration of experts in VW-MRI and/or GCA.

Orbital Myositis after Herpes Zoster Ophthalmicus: A Case Report and a Narrative Review of the Literature.

Herpes zoster ophthalmicus results from the reactivation of the latent varicella zoster virus, affecting the first branch of the trigeminal nerve. In 20-70% of cases, Zoster Ophthalmicus can lead to ocular involvement, affecting various orbital structures. Orbital myositis is a rare but severe complication of herpes zoster ophthalmicus. We present a case of a 52-year-old man with no significant medical history who developed zoster-associated right ocular myositis and dacryocystitis. He was treated with intravenous acyclovir and oral steroids. A review of the literature identified 29 patients across 19 studies. The median age was 61 years, with a slight female predominance. In 55% of cases, the patients had no notable medical history. The most common presentation of myositis involved all oculomotor muscles. There were 22 cases who were treated with intravenous antiviral therapy and 19 received steroids. A full resolution of symptoms was achieved in 51.7% of patients. Zoster-related orbital myositis is a rare complication that should be considered even in immunocompetent individuals. It may occur either before or after the appearance of a vesicular rash. Magnetic resonance imaging is the preferred radiological exam for assessing orbital involvement. Intravenous antiviral therapy should be started within 72 h of symptom onset, and its combination with systemic corticosteroids appears to be an effective treatment for zoster-related ocular myositis.

Schwarzschild modelling of barred s0 galaxy NGC 4371

ABSTRACT We apply the barred Schwarzschild method developed by Tahmasebzadeh et al. (2022) to a barred S0 galaxy, NGC 4371, observed by IFU instruments from the TIMER and ATLAS3D projects. We construct the gravitational potential by combining a fixed black hole mass, a spherical dark matter halo, and stellar mass distribution deprojected from 3.6 μm S$^4$G image considering an axisymmetric disc and a triaxial bar. We independently modelled kinematic data from TIMER and ATLAS3D. Both models fit the data remarkably well. We find a consistent bar pattern speed from the two sets of models with $\Omega _{\rm p} = 23.6 \pm 2.8 \, \mathrm{km \, s^{-1} \, kpc^{-1} }$ and $\Omega _{\rm p} = 22.4 \pm 3.5 \, \mathrm{km \, s^{-1} \, kpc^{-1} }$, respectively. The dimensionless bar rotation parameter is determined to be $\mathcal {R} \equiv R_{\rm cor}/R_{\rm bar}=1.88 \pm 0.37$, indicating a likely slow bar in NGC 4371. Additionally, our model predicts a high amount of dark matter within the bar region ($M_{\rm DM}/ M_{\rm total}$$\sim 0.51 \pm 0.06$), which, aligned with the predictions of cosmological simulations, indicates that fast bars are generally found in baryon-dominated discs. Based on the best-fitting model, we further decompose the galaxy into multiple 3D orbital structures, including a BP/X bar, a classical bulge, a nuclear disc, and a main disc. The BP/X bar is not perfectly included in the input 3D density model, but BP/X-supporting orbits are picked through the fitting to the kinematic data. This is the first time a real barred galaxy has been modelled utilizing the Schwarzschild method including a 3D bar.

The MAGPI survey: orbital distributions, intrinsic shapes, and mass profiles for MAGPI-like eagle galaxies using Schwarzschild dynamical models

ABSTRACT Schwarzschild dynamical models are now regularly employed in large surveys of galaxies in the local and distant Universe to derive information on galaxies’ intrinsic properties such as their orbital structure and their (dark matter and stellar) mass distribution. Comparing the internal orbital structures and mass distributions of galaxies in the distant Universe with simulations is key to understanding what physical processes are responsible for shaping galaxy properties. However, it is first crucial to understand whether observationally derived properties are directly comparable with intrinsic ones in simulations. To assess this, we build Schwarzschild dynamical models for MUSE-like IFS (integral field spectroscopy) cubes (constructed to be like those obtained by the Middle Ages Galaxy Properties with Integral Field Spectroscopy, MAGPI survey) of 75 galaxies at $z \sim$ 0.3 from the eagle simulations. We compare the true particle-derived properties with the galaxies’ model-derived properties. In general, we find that the models can recover the true galaxy properties qualitatively well, with the exception of the enclosed dark matter, where we find a median offset of 48 per cent, which is due to the assumed Navarro–Frenk–White profile not being able to reproduce the dark matter distribution in the inner region of the galaxies. We then compare our model-derived properties with Schwarzschild models-derived properties of observed MAGPI galaxies and find good agreement between MAGPI and eagle: the majority of our galaxies (57 per cent) have non-oblate shapes within 1 effective radius. More triaxial galaxies show higher fractions of hot orbits in their inner regions and tend to be more radially anisotropic.

Challenges and Insights in the Diagnosis and Management of Orbital Tuberculosis: A Systematic Review of 113 Cases.

Orbital tuberculosis (O-TB) is an extremely rare manifestation of extra-pulmonary tuberculosis (TB), which affects orbital structures and causes very complex clinical scenarios that may simulate other pathologies affecting the orbit. Its diagnostic and therapeutic challenges are due to its rarity and lack of specificity on symptoms. This systematic review aims to give an in-depth analysis regarding the presentation of clinical features, diagnosis methods, treatment outcomes, and complications, enhancing the current understanding and management of O-TB.A systematic review was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses. Literature searches were conducted in PubMed and Scopus up to August 2024. The literature review included case series, case reports, and retrospective studies focusing on O-TB and involved a total of 113 cases from 12 studies. The extracted data were qualitatively synthesized regarding patient demographics, clinical presentations, diagnostic methods, treatment regimens, and the ensuing outcomes. The review found that O-TB mostly affects subjects with a mean age of 37.75 years, although there is a very wide age range of reported cases: 2-82 years with an almost equal gender distribution. The most common symptoms were vision impairment at71.68%, eyelid swelling at 9.73%, and exophthalmos at 5.31%. Imaging, especially with computed tomography (CT) scans in 60.18% of patients, along with histopathological confirmation and molecular biological confirmation positive in 46.02%, was the principal tool for diagnosis. In most cases, antitubercular therapy (ATT) was the mainstay of treatment, leading to complete resolution. However, 30.09% of these cases had some complications like glaucoma and cataracts that point to careful management and follow-up. O-TB still remains a diagnostic challenge due to its rarity and changing clinical presentations. Early diagnosis and identification, presently mainly through imaging and histopathological examination, is important for the management. This review shows the effectiveness of ATT in the treatment of O-TB but also brings out the need for better diagnostic facilities and uniformity in treatment protocols so that complications can be prevented and outcomes improved. Future studies must be directed toward the development of more sensitive diagnostic tools and the elucidation of immune responses in O-TB guiding better clinical practice.

Temporoparietal Fascial Flap Combined With Vascularized Outer Table Calvarial Bone Graft and Entire Temporalis Muscle: A Stable Pedicled Flap for Orbital Floor Reconstruction After Total Maxillectomy.

Orbital reconstruction after total maxillectomy is essential to maintain ocular function and facial contour. Free flap transfer with simultaneous orbital bone reconstruction is a straightforward approach; however, it is challenging in medically unstable patients with multimorbidity. The authors developed an easily harvested temporoparietal fascial flap combined with vascularized outer table calvarial bone and entire temporalis muscle. The authors applied this technique in an 81-year-old patient with multiple comorbidities who required orbital floor reconstruction following total maxillectomy. Intraoperative indocyanine green fluorescence imaging confirmed excellent perfusion of the temporoparietal fascia, entire temporalis muscle, and calvarial bone. Although the patient developed postoperative local wound infection, the vascularized bone graft resisted infection and preserved the orbital structure without bone exposure. Our technique is minimally invasive and results in a well-vascularized flap for orbital reconstruction after total maxillectomy involving the orbital bone, and particularly beneficial in patients with multimorbidity or at high risk of local infection.

Superior rectus/levator complex in acquired anophthalmic socket repaired with spheric implant-a computed tomography scan and topographic study.

To determine whether the levator palpebrae superioris (LPS)/superior rectus (SR) muscle complex, can influence the position of the upper lid and fornix in acquired anophthalmic sockets. This comparative non-randomized and non-interventional study included retrospective data of 21 patients with unilateral acquired anophthalmic sockets repaired with spheric implants. High-resolution computed tomography (CT) measurements of the LPM/SR muscle complex and clinical topographic position of the upper lid, superior and inferior fornix depth in primary gaze position were evaluated. Demographic data were presented as frequency and percentage proportions and quantitative variables comparing the socket measurements with the normal contralateral orbit was statistically analyzed using non-parametric tests considering P<0.05. The anophthalmic orbits had a significantly shorter LPS length (P=0.01) and significantly thicker SR (P=0.02) than the normal orbit. Lagophthalmos was present in anophthalmic sockets but not in normal orbits (P=0.002), while levator function was normal in both (P>0.05, all comparisons). The superior fornix depth was similar in the anophthalmic socket and the contralateral normal orbit (P=0.192) as well the inferior fornix depth (P=0.351). Acquired anophthalmic sockets repaired with spheric implants have shorter LPS, thicker SR, and more lagophthalmos than normal orbits. The relationship of the LPS and SR with other orbital structures, associated with passive or active forces acting in the final position of the lids and external ocular prosthesis should be further investigated.

Polychromatic electrochromic films via bipolar covalent organic framework design

Because of the ordered and loose structure, covalent organic framework (COF) holds broad promise in the field of electrochromism, but the simple color change limits its application and development. A bipolar and polychromatic COF-GZU1 was successfully designed and prepared in this paper. The structure, electrostatic potential and orbital structure of the COF-GZU1 were predicted and calculated using density functional theory, and the calculation results confirmed the feasibility of bipolar construction strategy. XRD, SEM, BET and GIWAXS further mutually established the successful synthesis of COF-GZU1, which exhibited high specific surface area, crystallinity and porosity. Results from electrochemical impedance spectroscopy, density of states analysis, and ion diffusion coefficient measurements verified that the ordered porous structure facilitates electron conduction and ion mass transfer, leading to a significant improvement in electrochromic performance. Moreover, the COF-GZU1 film displayed excellent electrochromic performance, providing polychromatic switching with a rapid response time (7.8/14.5 s and 1.0/12.6 s for coloring/bleaching process) and high coloring efficiency (112.8 and 127.8 cm2∙C-1 at 799 and 570 nm). These results collectively demonstrate the superiority of the COF-GZU1 film and suggest that the bipolar COF design strategy could pave the way for new and high-performance polychromatic electrochromic materials.

Photoelectron momentum distributions of triatomic CO2 molecules by circularly polarized attosecond pulses

Abstract Molecular-frame photoelectron momentum distributions (MF-PMDs) have been studied for imaging molecular structures. We investigate the MF-PMDs of CO2 molecules exposed to circularly polarized (CP) attosecond laser pulses by solving the time-dependent Schrödinger equations based on the single-active-electron approximation frames. Results show that high-frequency photons lead to photoelectron diffraction patterns, indicating molecular orbitals, these diffraction patterns can be illustrated by the ultrafast photoionization models. However, for the driving pulses with 30 nm, a deviation between MF-PMDs and theoretically predicted results of the ultrafast photoionization models is produced because the Coulomb effect strongly influences the molecular photoionization. Meanwhile, the MF-PMDs rotates in the same direction as the helicity of driving laser pulses. Our results also demonstrate that the MF-PMDs in a CP laser pulse are the superposition of those in the parallel and perpendicular linearly polarized cases. The simulations efficiently visualize molecular orbital geometries and structures by ultrafast photoelectron imaging. Furthermore, we determine the contribution of HOMO and HOMO-1 orbitals to ionization by varying the relative phase and the ratio of these two orbitals.

Atomristor Mott Theory of Sn Adatom Adlayer on a Si Surface

We use a combination of density functional theory (DFT) and dynamical mean field theory (DMFT) to unveil orbital field-induced electronic structure reconstruction of the atomic Sn layer deposited onto a Si(111) surface (Sn/Si(111)−3×3R30∘), also referred to as α-Sn. Our DFT + DMFT results indicate that α-Sn is an ideal testing ground to explore electric field-driven orbital selectivity and Mott memory behavior, all arising from the close proximity of α-Sn to metal insulator transitions. We discuss the relevance of orbital phase changes for α-Sn in the context of the current–voltage (I−V) characteristic for future silicon-based metal semiconductor atomristors.

Machine Learning Algorithms for Sex Classification by Using Variables of Orbital Structures: A Computed Tomography Study

Machine Learning Algorithms for Sex Classification by Using Variables of Orbital Structures: A Computed Tomography Study

OCCUPATIONAL AND ENVIRONMENTAL FACTORS ASSOCIATED WITH OCULAR TRAUMA AMONG PATIENTS ATTENDING EYE CARE SERVICES AT JINJA REGIONAL REFERRAL HOSPITAL. A CROSS-SECTIONAL STUDY.

Background Ocular trauma refers to any injury to the eyeball, its adnexa, orbit, and periorbital structures due to direct contact with fixed or mobile, blunt or sharp objects. The study aims to assess the factors associated with ocular trauma among patients attending eye care services at Jinja Regional Referral Hospital. Methodology A cross-sectional descriptive study design that collected quantitative data from 100 respondents using a non-probability consecutive sampling process from September 2022 to March 2023. Results 70% of the respondents were male while 30% were females. 55% of the respondents were 21-40 years, 32% were 0-20 years, 10% were 41-60 years and 3% were &gt;60 years. Ocular injuries were caused by a foreign body (40%) followed by work-related activities with 20%, accidents with 18%, assault-related actions with 20%, and the least were chemical injuries with 5%. (65%) didn’t have eye protective equipment while 35% had. 40% of the respondents knew about awareness programs on ocular trauma while 60% had not received these programs. (43%) obtained trauma from the workplace, 25% from bars, 17% from homes, and 15% from schools. 55% had used nontherapeutic drugs like alcohol. 50% were using water from protected streams, 30% were using water from taps, 15% were using water from wells and the least were those using water from rivers (05%). Conclusion The most affected age group was 21-40. Males were more affected than females. Literates were most affected, and most cases of ocular trauma were obtained from the workplace. Ocular trauma was associated with the use of non-therapeutic drugs like alcohol. Recommendations Health education on ocular injuries should be adopted by the relevant authorities to increase awareness of the dangers, causes, predisposing factors, and burden of ocular trauma in the community.

Comparison of Skull Morphometric Characteristics of Simmental and Holstein Cattle Breeds.

This study aimed to reveal the morphological characteristics of pure Holstein and Simmental skulls and to obtain reference values for morphometric analysis. Moreover, 54 skulls from 12- to 14-month-old male Holstein (n = 25) and Simmental (n = 29) cattle were collected from Turkey's Southeastern Anatolia Region between 2023 and 2024. Linear measurements indicated that Holsteins had longer skulls compared to Simmentals. Holsteins exhibited significantly higher values for the greatest length of nasals and the shortest skull length. The facial breadth was wider in Holsteins and statistically distinctive between the breeds. Holsteins had a more oval orbital bony roof, while Simmentals exhibited a wider orbital structure. The orbital index was higher in Holsteins, distinguishing between the two breeds. It was observed that Simmental cattle had a wider occipital region. This difference is likely due to the larger lateral appearance of the Simmental skull, which has more body weight and provides a larger surface area for muscle attachment. These differences not only aid in breed identification but also offer insights into the functional adaptations of each breed. Future research should explore the genetic and environmental factors contributing to these morphological traits, further enriching our knowledge of cattle morphology and its implications for breeding and conservation efforts.

One electron is enough: A chemical bonding approach on the hydrogen induced structural transformation in MPd3 (M = Mg, In, Tl) intermetallic compounds

It is crucial to understand the nature of the metal-hydrogen interactions in the intermetallic hydrides in order to develop new hydrogen storage materials with optimum metal-H interactions for desired hydrogen absorption-desorption kinetics. The MPd3 intermetallic compounds (M = Mg, In, Tl) transform to cubic anti-perovskite type (AuCu3-type with hydrogen in the octahedral intersect) structure from ZrAl3-type four-fold ccp-superstructure up on hydrogenation. According to the DFT-based orbital space electronic structure and chemical bonding analysis, this structural transformation is driven by maximizing the coordination of hydrogen surrounded by Pd, forming the Pd (4d) – H (1s), and … Pd–H–Pd … multicenter interactions. These interactions provide sufficient thermodynamic stability for the hydrides to form, with negative binding energies of hydrogen. The binding energies are found to be significantly low, with the possibility of the ease of hydrogen desorption within limited reaction conditions.

Методика балістичного планування місій низькоорбітального сервісного обслугову-вання з малою постійною тягою рушійних систем

The current stage of space exploration is characterized by an increased interest in the development, deployment, and operation of low-orbit satellite constellations (LOSC) for Earth and near-Earth space remote sensing for military and civilian purposes and for global and regional satellite communications. Reusable space launch vehicles have significantly reduced the orbital injection cost. As a result, satellite operators are developing and deploying large-scale LOSCs of various orbital structures with a large number of spacecraft. According to current estimates, more than 70% of all the operating satellites operate in low-Earth orbits (LEOs) at altitudes between 160 km and 2,000 km. Since LEO satellites are generally much cheaper than satellites in geostationary orbits, the possibility of their on-orbit servicing (OOS) has not been the focus of research. However, the use of LEO OOS has prospects for growth. Techniques for ballistic planning of LEO OOS missions have been and are being developed. The disadvantages of approximate techniques include the use of simplified flight dynamics models. Most of the existing exact techniques are based on the use of full mathematical models of flight dynamics and the shooting method to solve the boundary value problem of an orbit transfer. Using the shooting method requires a sufficiently accurate initial guess, which is difficult to determine. To obtain a second approximation, use is mainly made of optimization methods, which do not always find a global minimum. In this regard, there is a need to develop new techniques that would be free from the above disadvantages. The goal of the article is to develop a ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems. The technique includes the identification of LEO areas promising for OOS, a mathematical model of the dynamics of perturbed OOS orbit transfers in modified equinoctial orbital elements, and a solution algorithm for the boundary value problem of determining the control parameters of perturbed OOS low-orbit transfers. The problem is solved using methods of statistical analysis, flight dynamics, shooting, genetic optimization, and mathematical simulation. The novelty lies in the identification of LEO areas promising for OOS and the development of a mathematical model of orbit transfer dynamics in modified equinoctial orbital elements and a solution algorithm for determining the control parameters of perturbed OOS low-orbit transfers. The results of the work may be used in the justification and planning of LEO OOS missions and the formulation of requirements for LEO OSS mission propulsion systems.

Electronic structure and resonant inelastic x-ray scattering in Ca3Ru2O7

We have investigated the electronic structure of the transition metal oxide Ca3Ru2O7 within density-functional theory using the generalized gradient approximation while considering strong Coulomb correlations in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band structure method. Ca3Ru2O7 can be classified as a Mott insulator since it was expected to be metallic from band structure calculations. We found that the magnetic ground state of Ca3Ru2O7 possesses an AFM−b magnetic structure with the Ru spin moments ordered antiferromagnetically along the b axis. We have investigated the resonant inelastic x-ray scattering (RIXS) spectra at the Ru and Ca K, L3, and M3 edges as well as at the OK edge. The experimentally measured RIXS spectrum of Ca3Ru2O7 at the Ru L3 edge possesses a sharp feature ≤2eV corresponding to transitions within the Ru t2g levels. The excitation located from 2 to 4 eV is due to t2g→ eg transitions. The third wide structure situated at 4.5−11eV appears due to transitions between the Ru 4dO states derived from the tails of oxygen 2p states and eg and t2g states. The RIXS spectra at the Ru L3 and M3 edges are quite similar. However, the corresponding RIXS spectra at the Ca site are quite different from each other due to the significant difference in the widths of core levels. The RIXS spectrum at the OK edge consists of three major inelastic excitations. We found that the first two low energy features ≤2.5eV are due to interband transitions between occupied and empty Ot2g states which appear due to the strong hybridization between oxygen 2p and Ru t2g states in close vicinity to the Fermi level. The next major peak between 2.5 and 8 eV reflects interband transitions from occupied O2p to empty Ot2g states. A wide energy interval between 4 and 11 eV is occupied by rather weak O2p→Oeg transitions. Published by the American Physical Society 2024

Bifurcations of phase portraits and chaotic behaviors of the (2+1)-dimensional double‐chain DNA system with beta derivative: A qualitative approach

Qualitative analysis in mathematical modeling has become an important research area within the broad domain of nonlinear sciences. In the realm of qualitative analysis, the bifurcation method is one of the significant approaches for studying the structure of orbits in nonlinear dynamical systems. To apply the bifurcation method to the (2 + 1)-dimensional double-chain Deoxyribonucleic Acid system with beta derivative, the bifurcations of phase portraits and chaotic behaviors, combined with sensitivity and multi-stability analysis of this system, are examined. Initially, the bifurcations of phase portraits are visually identified at the obtained equilibrium points of a planar dynamical system via both Hamiltonian and Jacobian algorithms. The obtained results indicate Jacobian algorithm is more efficient in identifying the stability of bifurcations than the Hamiltonian algorithm for this system. Subsequently, by introducing an external perturbation term into the planar dynamical system, the chaotic behavior is effectively identified by using a variety of tools, such as two- and three-dimensional phase portraits, time series, Lyapunov exponents, and Poincaré maps. The findings suggest that the perturbed dynamical system deviates from regular patterns and exhibits behavior ranging from periodic to quasi-periodic and from quasi-periodic to chaotic. Finally, the sensitivity and multi-stability of the system are examined using the Runge-Kutta method to assess the model's response to minor variations in initial conditions through numerical solutions, revealing that the model is sensitive and multi-stable. The outcomes of this study will enhance a relationship between applied mathematicians and experimental biologists, helping to explore hidden features of Deoxyribonucleic Acid through the studied model.