Conformal Mapping Research Articles

Bouncing and collapsing universes dual to late-time cosmological models

We use the Jordan frame–Einstein frame correspondence to explore dual universes with contrasting cosmological evolutions. We study the mapping between Einstein and Jordan frames where the Einstein frame universe describes the late-time evolution of the physical universe, which is driven by dark energy and non-relativistic matter. The Brans–Dicke theory of gravity is considered to be the dual scalar–tensor theory in the Jordan frame. We show that an Einstein frame universe, with cosmological evolution of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model, always corresponds to a bouncing Jordan frame universe governed by a Brans–Dicke theory. On the other hand, quintessence models of dark energy with non-relativistic matter component are shown to be always dual to a Brans–Dicke Jordan frame with a turn-around, i.e., a bounce or a collapse. The evolution of the equation of state of the quintessence field determines whether the turn-around is a bounce or a collapse. The point of the Jordan frame turn-around for all the cases can be tuned anywhere by choosing an appropriate Brans–Dicke parameter. This essentially leads to alternative descriptions of the late-time evolution of the physical universe, in terms of bouncing or collapsing Brans–Dicke universes in the Jordan frame. Therefore, the effect of dark energy can equivalently be seen as collapse of space in a conformally connected universe. We further study the stability of such conformal maps against linear perturbations. The effective bouncing and collapsing descriptions of the current accelerating universe may have interesting implications for the evolutions of perturbations and quantum fluctuations in the cosmological background.

A new approach from the calculus of variations to the Lichnerowicz theorem

The well-known Lichnerowicz theorem states that on an n-dimensional compact Riemannian manifold without boundary with the assumptionRicg≥(n−1)g on the Ricci curvature, the first eigenvalue λ of the Laplacian on the manifold satisfiesλ≥n. This theorem is proved using a Bochner formula.In this paper we give a new approach from the calculus of variations to the Lichnerowicz theorem. We use the energy Econf() of conformality, introduced in [3]. For a smooth map f between Riemannian manifolds, the map f is a weakly conformal map (almost everywhere) if and only if Econf(f) = 0 (the minimum value).Our approach is as follows:(1)The identity map on M is a conformal map, hence a minimizer of the energy Econf(). Especially the identity map is stable, i.e., the second variation is non-negative for the identity map.(2)For the first eigenfunction φ, we take the variation vector field corresponding to dφ, and the non-negativity of the second variation for the variation vector field at the identity map implies the Lichnerowicz theorem.

Synthesis, in vitro, and in silico studies of morpholine-based thiosemicarbazones as ectonucleotide pyrophosphatase/phosphodiesterase-1 and -3 inhibitors

An extensive range of new biologically active morpholine based thiosemicarbazones derivatives 3a-r were synthesized, characterized by spectral techniques and evaluated as inhibitors of ENPP isozymes. Most of the novel thiosemicarbazones exhibit potent inhibition towards NPP1 and NPP3 isozymes. Compound 3 h was potent inhibitor of NPP1 with IC50 value of 0.55 ± 0.02. However, the most powerful inhibitor of NPP3 was 3e with an IC50 value of 0.24 ± 0.02. Furthermore, Lineweaver-Burk plot for compound 3 h against NPP1 and for compound 3e against NPP3 was devised through enzymes kinetics studies. Molecular docking and in silico studies was also done for analysis of interaction pattern of all newly synthesized compounds. The results were further validated by molecular dynamic (MD) simulation where the stability of conformational transformation of the best protein-ligand complex (3e) were justified on the basis of RMSD and RMSF analysis.

Estimates for a class of analytic and univalent functions connected with quasi-subordination

Geometric Function Theory, an active field of studied that has its roots in complex analysis, has gained an impressive attention from many researchers. This occurs largely because it deals with the study of geometric properties of analytic (and univalent) functions where many of its applications spread across many fields of mathematics, mathematical physics and engineering. Notable areas of application include conformal mappings, special functions, orthogonal polynomials, fluid flows in physics and engineering designs. The investigations in this paper are on a subclass of analytic and univalent functions defined in the unit disk Ω and denoted by Qaq(m). The definition of the new class encompasses some well-known subclasses of analytic and univalent functions such as the classes of starlike functions, Yamaguchi functions, and Ma-Minda functions. Two key mathematical principles involved in the definition of the class are the principles of Taylor’s series and quasi-subordination. Some of the investigations carried out on functions f ∈ Qaq(m) are however, the upper estimates for some initial bounds, the solution to the well-known Fekete-Szego problem and the upper estimate for a Hankel determinant.

Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces

Surface parameterization plays a fundamental role in many science and engineering problems. In particular, as genus-0 closed surfaces are topologically equivalent to a sphere, many spherical parameterization methods have been developed over the past few decades. However, in practice, mapping a genus-0 closed surface onto a sphere may result in a large distortion due to their geometric difference. In this work, we propose a new framework for computing ellipsoidal conformal and quasi-conformal parameterizations of genus-0 closed surfaces, in which the target parameter domain is an ellipsoid instead of a sphere. By combining simple conformal transformations with different types of quasi-conformal mappings, we can easily achieve a large variety of ellipsoidal parameterizations with their bijectivity guaranteed by quasi-conformal theory. Numerical experiments are presented to demonstrate the effectiveness of the proposed framework.

Delineating the impact of N21D mutation on the conformational preferences and structural transitions in human islet amyloid polypeptide

The amyloid deposits of human islet amyloid polypeptide (hIAPP) in the pancreatic β-cells are linked to a chronic metabolic disease known as type 2 diabetes (T2D). Recent studies reported that N21D mutation in hIAPP inhibited the formation of fibrillar aggregates, however, the underlying molecular mechanism of fibril inhibition in the N21D mutant remains largely unclear. Thus, molecular dynamics (MD) simulations have been employed to illuminate the effect of N21D mutation on the conformational dynamics and structural transformations in hIAPP at the atomistic level. Notably, the structural stability of WT-hIAPP (wild type-hIAPP) was enhanced upon N21D mutation. Interestingly, the sampling of helical conformation in hIAPP was significantly increased from 12.60 to 19.80% with a concomitant decrease in β-sheet from 7.40 to 1.20% upon N21D mutation that corroborates with the circular dichroism (CD). The dihedral principal component analysis (dPCA) depicted a notable reduction in the conformational phase space of [N21D]hIAPP as compared to WT-hIAPP, which highlights the prevention of conformational transitions and enhanced structural stability. Remarkably, a complete loss in the β-sheet content was noted in the conformations extracted from the free energy landscape of [N21D]hIAPP as compared to 24–25% sampling of β-sheets in minimum energy conformations of WT-hIAPP consistent with the transmission electron microscopy (TEM) and thioflavin T (ThT) fluorescence assay. The present study provided key insights into the N21D mutation-induced conformational changes in hIAPP and highlighted that Asn21 plays a key role in hIAPP aggregation. The insights from this work will be beneficial in the design of drug candidates by selectively targeting Asn21 of hIAPP which could interfere with its aggregation and associated cytotoxicity.

Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group

The asymptotic symmetry group of general relativity in asymptotically flat spacetimes can be extended from the Bondi-Metzner-Sachs (BMS) group to the generalized BMS (GMBS) group suggested by Campiglia and Laddha, which includes arbitrary diffeomorphisms of the celestial two-sphere. It can be further extended to the Weyl BMS (BMSW) group suggested by Freidel, Oliveri, Pranzetti and Speziale, which includes general conformal transformations. We compute the action of fully nonlinear BMSW transformations on the leading order Bondi-gauge metric functions: specifically, the induced metric, Bondi mass aspect, angular momentum aspect, and shear. These results generalize previous linearized results in the BMSW context by Freidel et al., and also nonlinear results in the BMS context by Chen, Wang, Wang and Yau. The transformation laws will be useful for exploring implications of the BMSW group.

Thermal analysis of a perforated laminated plate with multiple random elliptical holes by specially formulated finite elements

The high-efficient and accurate analysis of anisotropic composite media weakened by a large amount of holes or cuts is still a great challenge in practical composite engineering. In this work, specially-proposed polygonal finite element enclosing an arbitrarily oriented elliptical hole in general anisotropic composite media is formulated for thermal analysis in the framework of hybrid finite element theory. Two independent temperature field approximations are defined for the present special element: Intra-element temperature field and element frame temperature field. The former defined inside the element is written in the form of truncated summation of the weighted special fundamental solutions, which are derived using the Stroh complex theory and conformal mapping whilst the latter is implemented by the conventional shape function interpolation. Then the hybrid variational functional is employed to combine them together to generate an element stiffness equation with respect to nodal temperature and an optional relationship between the interpolation coefficients. The element stiffness matrix is symmetric and involves element boundary integrals only. Compared to the traditional finite element, the distinctive element-boundary-integral and enclosed-elliptical-hole features make the present element significantly improve the meshing effort around an elliptical hole by reducing the number of elements and decreasing the meshing difficulty, and more importantly, effectively capture the critical variation of physical fields around the elliptical hole without locally-refined meshes. Moreover, the present special element can be incorporated directly into the conventional finite element system without any difficulty for extensive analysis. Finally, several typical examples are simulated by the present special elements to demonstrate their effectiveness.

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.

Structures and Dynamics of β-Rich Oligomers of ATTR (105-115) Assembly.

Transthyretin (TTR) is a tetrameric homologous protein that can dissociate into monomers. Misfolding and aggregation of TTR can lead to amyloid transthyretin amyloidosis (ATTR), which can cause many diseases (e.g., senile systemic amyloidosis, familial amyloid cardiomyopathy, and familial amyloid polyneuropathy). Despite growing evidence indicating that small oligomers play a critical role in regulating cytotoxicity, the structures of these oligomeric intermediates and their conformational transformations are still unclear, impeding our understanding of neurodegenerative mechanisms and the development of therapeutics targeting early aggregation species. The TTR monomer protein consists of various fragments prone to self-aggregation, including the residue 105-115 sequence. Therefore, our study investigated the assembly progress of ATTR (105-115) peptides using all-atom molecular dynamics simulations. The findings indicate that the probability of β-sheet content increases with increasing numbers of peptides. Additionally, interactions between hydrophobic residues L110 and L111 are crucial for the formation of a β-rich oligomer formation. These β-rich oligomers may adopt β-barrel conformations, potentially toxic oligomer species. Free-energy analysis reveals that β-barrel conformations serve as intermediates for these β-rich oligomers. Our insights into the structural ensemble dynamics of ATTR (105-115) contribute to understanding the physical mechanisms underlying the β-barrel oligomers of ATTR. These findings may shed light on the pathological role of ATTR in neurodegenerative diseases and offer potential therapeutic targets.

Unveiling All‐Optical Switching Phenomenon in Anthracene Derivatives: A Comprehensive Study on Optical and Nonlinear Optical Multifunctionality

AbstractIn this study, it is considered three anthracene derivatives, characterized meticulously in terms of their chemical structure and product purity. Extensive quantum chemical calculations are conducted to elucidate their optical and nonlinear optical properties, shedding light on the mechanism of photoinduced conformational transformation, a pivotal discovery in this research. Experimental analyses encompassed fundamental optical properties and advanced nonlinear optical phenomena, including z‐scan experiments, second harmonic generation (SHG), and third harmonic generation (THG). Remarkably, a groundbreaking all‐optical switching phenomenon in these materials is experimentally validated, marking a significant advancement and contributing to their potential applications.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

Conformal and approximate analysis of the effect of cutoff wall thickness on finite depth seepage characteristics

ABSTRACT An analytical solution to the problem of two-dimensional steady-state seepage flow beneath a water-retaining structure is presented using conformal mapping and complex variables. This paper addresses the question of to what extent the cut-off thickness affects the values of seepage characteristics. The closed-form analytical equations are calculated numerically. The analytical results have been validated by comparing them with the available exact solutions for finite-depth seepage. The resulting implicit equations, involving elliptic integrals, are used to create design diagrams. Increasing the thickness can cause a reduction in hydraulic gradient, seepage discharge, and uplift pressure at the left tip of the cut-off. A customized fragment type considering the cut-off’s thickness is developed using the analytical results to estimate seepage quantities and exit gradients. The form factor for this fragment is obtained in the form of dimensionless charts, which predict the flow rate and exit gradient more precisely than the existing solutions.

Novel β-Hairpin Antimicrobial Peptide Containing the β-Turn Sequence of -NG- and the Tryptophan Zippers Facilitate Self-Assembly into Nanofibers, Exhibiting Excellent Antimicrobial Performance.

Antimicrobial peptides (AMPs) have emerged as promising agents to combat the antibiotic resistance crisis due to their rapid bactericidal activity and low propensity for drug resistance. However, AMPs face challenges in terms of balancing enhanced antimicrobial efficacy with increased toxicity during modification processes. In this study, de novo d-type β-hairpin AMPs are designed. The conformational transformation of self-assembling peptide W-4 in the environment of the bacterial membrane and the erythrocyte membrane affected its antibacterial activity and hemolytic activity and finally showed a high antibacterial effect and low toxicity. Furthermore, W-4 displays remarkable stability, minimal occurrence of drug resistance, and synergistic effects when combined with antibiotics. The in vivo studies confirm its high safety and potent wound-healing properties at the sites infected by bacteria. This study substantiates that nanostructured AMPs possess enhanced biocompatibility. These advances reveal the superiority of self-assembled AMPs and contribute to the development of nanoantibacterial materials.

Methotrexate for Drug Repurposing as an Anti-Aggregatory Agent to Mercuric Treated α-Chymotrypsinogen-A.

Protein aggregation is related to numerous pathological conditions like Alzheimer's and Parkinson's disease. In our study, we have shown that an already existing FDA-approved drug; methotrexate (MTX) can be reprofiled on preformed α-chymotrypsinogen A (α-Cgn A) aggregates. The zymogen showed formation of aggregates upon interaction with mercuric ions, with increasing concentration of Hg2Cl2 (0-150 µM). The hike in ThT and ANS fluorescence concomitant with blue shift, bathochromic shift and the hyperchromic effect in the CR absorbance, RLS and turbidity measurements, substantiate the zymogen β-rich aggregate formation. The secondary structural alterations of α- Cgn A as analyzed by CD measurements, FTIR and Raman spectra showed the transformation of native β-barrel conformation to β-inter-molecular rich aggregates. The native α- Cgn A have about 30% α-helical content which was found to be about 3% in presence of mercuric ions suggesting the formation of aggregates. The amorphous aggregates were visualized by SEM. On incubation of Hg2Cl2 treated α- Cgn A with increasing concentration of the MTX resulted in reversing aggregates to the native-like structure. These results were supported by remarkable decrease in ThT and ANS fluorescence intensities and CR absorbance and also consistent with CD, FTIR, and Raman spectroscopy data. MTX was found to increase the α-helical content of the zymogen from 3 to 15% proposing that drug is efficient in disrupting the β-inter-molecular rich aggregates and reverting it to native like structure. The SEM images are in accordance with CD data showing the disintegration of aggregates. The most effective concentration of the drug was found to be 120 µM. Molecular docking analysis showed that MTX molecule was surrounded by the hydrophobic residues including Phe39, His40, Arg145, Tyr146, Thr151, Gly193, Ser195, and Gly216 and conventional hydrogen bonds, including Gln73 (bond length: 2.67Å), Gly142 (2.59Å), Thr144 (2.81Å), Asn150 (2.73Å), Asp153 (2.71Å), and Cys191 (2.53Å). This investigation will help to find the use of already existing drugs to cure protein misfolding-related abnormalities.

Bounds on geometric wakefields in collimators and step transitions of arbitrary cross sections

We present the wakefield conformal mapping technique that can be readily applied to the analysis of the radiation generated by an ultra-relativistic particle in the step transition and a collimator. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections and can become a useful tool in the shape optimization problems.

Unusual bending patterns of spermidine3+ bound to DNA double helix

Natural polyamines play a fundamental role in the cell cycle. Despite being recognized as the most abundant organic counterions of DNA in the cell nucleus, their interactions with DNA have not been fully characterized. In a recent work [S. Perepelytsya, T. Vasiliu, A. Laaksonen, L. Engelbrecht, G. Brancato, and F. Mocci, J. Molec. Liq.389, 122828 (2023)], we have shown how the interactions between spermidine3+ and the DNA double helix induce significant conformational variations in the polyamine molecule. Specifically, we found that DNA induces conformations that are not observed in solution. Following that study, we present here a detailed investigation of the most compact conformation of the polyamine, analyzing its connection to the interaction with the DNA duplex. The analysis reveals that anomalous bent conformations of the spermidine3+ molecule result from the interaction of all three amino groups of the polyamine with the DNA phosphate groups on the minor groove side of the double helix. The changes in dihedral angles of the bent spermidine3+ molecule can be explained in terms of conformational transformations of six- and seven-membered rings, analogous to cyclohexane and cycloheptane. The analysis of the position of spermidine3+ molecule along the DNA surface reveals a sequence specificity of this binding mode with a marked preference for the narrow minor groove of A-tracts. The formation of the anomalous bent conformations of spermidine3+ in the complex with the DNA double helix is expected to be of paramount importance in understanding the mechanisms underlying DNA’s biological function.

Thermodynamics of black holes charged with a conformally invariant electrodynamics in (n+1)-dimensional scalar-tensor theory

The Jordan frame (JF) field equations of scalar-tensor (ST) theory are strongly coupled and, the exact solutions cannot be obtained easily. By using the conformal transformation (CT), the ST action has been translated to the Einstein frame (EF) where the theory is known as the Einstein-dilaton (Ed) gravity. Also, an [Formula: see text]-dimensional electromagnetic Lagrangian has been introduced which remains invariant under CT. The Ed-conformal-invariant field equations, which are confronted with the mathematical indeterminacy problem, have been solved by use of a power-law ansatz function. We have introduced two classes of black holes (BHs) which are asymptotically non-flat and non-AdS. The Ed exact solutions can produce BHs with three, two, one and without horizons. By calculating the thermodynamic quantities, and making use of the Smarr mass relation it has been shown that the thermodynamical first law is valid in the EF. Thermal stability of Ed BHs has been analyzed by considering specific heats, thermodynamic Ricci scalars and Gibbs free energies, separately. Then using the inverse CTs, the ST exact solutions have been obtained which show two classes of horizonless, one-horizon, two-horizon and three-horizon BHs. We found that CTs preserve thermodynamic quantities and, thermodynamic properties of the ST BHs are just like those of Ed ones.

Anion‐modulated Ion Conductor with Chain Conformational Transformation for Enhanced Interfacial Phase Stabilization of High‐Voltage Lithium Metal Batteries

In solid‐state lithium metal batteries (SSLMBs), the inhomogeneous electrolyte‐electrode interphase layer aggravates the interfacial stability, leading to discontinuous interfacial ion/charge transport and continuous degradation of the electrolyte. Herein, we constructed an anion‐modulated ionic conductor (AMIC) that enables in‐situ construction of electrolyte/electrode interphases for high‐voltage SSLMBs by exploiting conformational transitions under multiple interactions between polymer and lithium salt anions. Anions modulate the decomposition behavior of supramolecular poly(vinylidene chloride) (PVC) at the electrode interface by changing the spatial conformation of the polymer chains, which further enhances ion transport and stabilizes the interfacial morphology. In addition, the AMIC weakens the “Li+‐solvation” and increases Li+ vehicle sites, thereby enhancing the lithium‐ion transport number (tLi+ = ~0.67). Consequently, Li||LiNi0.8Co0.1Mn0.1O2 cell maintains about 85% capacity retention and Coulombic efficiency > 99.8% in 200 cycles at a charge cut‐off voltage of 4.5V. This study provides a new understanding of lithium salt anions regulating polymer chain segment behavior in the SPE and highlights the importance of the ion environment in participating in the construction of interfacial phases and ionic conduction.

Molecular Serum Albumin Unmask Nanobio Properties of Molecular Graphenes in Shungite Carbon Nanoparticles.

Serum albumin is a popular macromolecule for studying the effect of proteins on the colloidal stability of nanoparticle (NP) dispersions, as well as the protein-nanoparticle interaction and protein corona formation. In this work, we analyze the specific conformation-dependent phase, redox, and fatty acid delivery properties of bovine albumin in the presence of shungite carbon (ShC) molecular graphenes stabilized in aqueous dispersions in the form of NPs in order to reveal the features of NP bioactivity. The formation of NP complexes with proteins (protein corona around NP) affects the transport properties of albumin for the delivery of fatty acids. Being acceptors of electrons and ligands, ShC NPs are capable of exhibiting both their own biological activity and significantly affecting conformational and phase transformations in protein systems.