arXiv subjects

Elshad Allahyarov

Publications and source records attributed to Elshad Allahyarov.

At least 19 recordsLinked to original sources

arXiv2026

Molecular Transferability of a Noble-Gas Coordinate for Electronegativity Equalization

Charge-equilibration models predict how electrons redistribute over a molecule more cheaply than quantum chemistry, and each begins from a table of atomic electronegativities and hardnesses. A recent table replaces ionization energies and electron affinities with one geometric quantity: each main-group atom's fractional distance to the noble gas closing its row. Holding geometries, electrostatic damping and the molecule list fixed, we compare it with spectroscopic values, with its own kernel refitted, and with a quadratic control, over a primary set of fifty-two molecules and ions at the B3LYP/def2-TZVP level. Two structural consequences follow from the table construction rather than the equalization solver. Atoms at equal fractional distance receive identical electronegativities, so the dipole moments of chlorine monofluoride, iodine monobromide and sulfur dioxide vanish exactly, and the measured $0.72$ debye $\mathrm{HF}/\mathrm{HCl}$ gap is lost. Because the first period is excluded, hydrogen retains its spectroscopic electronegativity above every geometric value, reversing $\mathrm{O{-}H}$, $\mathrm{N{-}H}$ and hydrogen-halide polarity. Fitted alike, geometric and quadratic kernels agree to $0.0022$ electron per atom, so predictions are set by the fitted energy scales, not the kernel shape. Resolving the electronegativity scale period by period restores correct polarity in all five polyatomic heavy-atom-hydrogen tests.

physics.chem-ph↗

arXiv2026

Tilt control of coverage heterogeneity for hard spherocylinders locked on a sphere

We study hard spherocylinders on a sphere with axes rigidly locked to a tangential director field at fixed angle $\tilt$ to the meridian, necessarily singular at the poles. Three lengths set the problem: the rod length $\Lrod$, the diameter $\Drod$, and the host radius $\Rsph$. Monte Carlo simulations across fifteen geometries and four coverages give two main results for the polar marginal, the azimuthal average of rod-center density. First, the tilt is a continuous handle on the width of the depleted region that packing induces around each singularity. Under meridian locking it is set principally by the rod length; turning the director toward the latitude contracts it substantially, the contraction being spent well before latitude locking. Second, how uniform the polar marginal can be made is limited by geometry, not tilt. The smallest variance on the sampled grid follows a power law in $\Lrod^{2}/(\Rsph\Drod)$, which measures how far a straight rod's ends stand off the curved surface in rod diameters, with an effective exponent between $1.1$ and $1.3$. Long rods on small hosts cannot be made uniform at any sampled tilt; the remedy is geometric, not orientational. The polar marginal is equator-heavy almost everywhere, inverting only at high coverage and tilt; meridian locking is the least uniform choice, and the variance-minimizing tilt usually lies in a sampled band from $31.7^{\circ}$ to $55^{\circ}$. The golden-ratio tilt $\arctan(1/\phigold)$ is one of those angles: a benchmark, not one the model selects. Both results describe the infinitely locked athermal ensemble.

cond-mat.soft↗

arXiv2026

Curvature-induced smectic-C order of tangentially anchored hard spherocylinders on a sphere with a rigidly locked director field

We study the strict locked-orientation limit of hard spherocylinders on a sphere, in which the rod axes are rigidly locked to a prescribed tangential director field and cannot reorient. Because the bulk hard-rod phase diagram contains no smectic-C phase, any coherent tilt isolates a geometric curvature mechanism rather than a finite-stiffness equilibrium effect. A ratio-symmetric recognition cost fixes the layer spacing at the bulk close-contact value and yields a hierarchy of geometric statements: the lower edge of the smectic-area window at $45^\circ$ follows from reciprocal symmetry; the upper edge at $58.3^\circ$ is a falsifiable channel-saturation hypothesis; the smectic-A to smectic-C boundary is a closed-form prediction; and the rod tilt angle is set by the rod-to-radius ratio, modulated by a chirality envelope peaking near $24^\circ$. Locked-orientation Monte Carlo across fifteen geometries confirms these predictions with no fitted elastic constants: the smectic area peaks at $55^\circ$, and a coherent smectic-C window is detected.

cond-mat.soft↗

arXiv2026

A Noble-Gas-Centered Coordinate for Within-Period Atomic Property Trends

We introduce a single dimensionless landscape function $J_{\rm chem}(ρ) = \cosh(ρ\ln φ) - 1$, $φ= (1+\sqrt{5})/2$, on the noble-gas-centred coordinate $ρ= d/L_p \in [0,1)$, and show that it organizes four central atomic observables: first ionization energy \IE$_1$, electron affinity EA, Mulliken electronegativity $χ_M$, and Pearson chemical hardness $η$, on one periodic-table axis. The outward step $ΔJ_{\rm chem}^{+}$ delivers IE$_1$; the inward gap $ΔJ_{\rm chem}^{-} = J_{\rm chem}(1) - J_{\rm chem}(ρ)$ delivers EA and $η$; $χ_M$ follows by Mulliken's identity. Three results establish the empirical content. (i) The within-period IE$_1$ envelope reproduces the full noble-gas-to-alkali ordering across periods 2--6: of 34 atoms compiled across periods 2-4, 26 lie on the predicted monotone descent and the 8 upward deviations occur exactly at the textbook anomaly sites $\{p^3, d^5, f^7, s^2, d^{10}\}$. (ii) Two golden-ratio identities, ${\rm IE}_1(G_p)/{\rm IE}_1(G_{p+1}) \approx φ^{1/4}$ on three heavy noble-gas pairs and ${\rm IE}_1(\text{halogen})/{\rm IE}_1(\text{alkali}) \approx φ^2$ on four within-period pairs, agree with NIST data to MAD $\approx 1\%$ and $\approx 5\%$, respectively. (iii) The shared kernel $ΔJ_{\rm chem}^{-}$ provides single-parameter analytical fits to EA across periods 4--6 (MAE $0.3$--$0.4$~eV), to Pearson hardness $η$ across periods 2--4 (MAE $\sim 1$~eV on noble-gas maxima up to $10.8$~eV), and to Mulliken $χ_M$ across a 15-atom four-class benchmark ($R^2 = 0.73$). \edit{At the period-averaged scale level, the shared-kernel relation ${\rm EA}/η\approx C^{(p)}_{\mathrm{EA}}/C^{(p)}_η$ is supported on period-4 NIST data: the empirical nine-atom mean $\overline{{\rm EA}/η} = 0.180$ agrees with the predicted constant $0.182$ to better than $1\%$, although individual-atom scatter ($σ\approx 0.13$) is much larger.

physics.chem-ph↗

arXiv2026

The d'Alembert Inevitability Theorem

We study functions satisfying the composition law $F(xy)+F(x/y)=P(F(x),F(y))$ with a symmetric polynomial combiner $P$. We prove that symmetry together with a quadratic degree bound on $P$ forces a composition law of d'Alembert type. We establish a degree mismatch exclusion criterion showing that symmetric polynomial combiners with $\mbox{deg} P(u,v) \ge 3$ do not admit nonconstant continuous solutions, provided the leading term does not cancel (Theorem 3.1.). For continuous nonconstant functions $F:\mathbb{R}_{>0}\to\mathbb{R}$ with $F(1)=0$ satisfying the composition law with a symmetric polynomial $P$ of degree at most two, the combiner is necessarily of the form $P(u,v)=2u+2v+c\,uv$, $c\in\mathbb{R}$ (Theorem 3.3.). The equation reduces in logarithmic coordinates to the classical d'Alembert functional equation. For $c\neq 0$, one obtains hyperbolic or trigonometric branches, while $c=0$ yields the squared-logarithm family. Under the cost-function assumptions $F\ge 0$ and convexity, only the hyperbolic branch with $c>0$ remains. A unit log-curvature calibration selects the canonical value $c=2$, which yields the canonical reciprocal cost $F(x)=\tfrac12(x+x^{-1})-1$. For $c\neq0$, the result extends to $\mathbb{R}_{>0}^n$: every solution depends only on a single linear combination of coordinate logarithms; for $c=0$, the solution is a general quadratic form $\sum_{i,j}a_{ij}\ln x_i\ln x_j$. In either case, nontrivial coordinate-wise separable costs are excluded.

math.CA↗

arXiv2026

A Complete Derivation of the Fermion Spectrum from the Recognition Composition Law

We present a first-principles derivation of the masses of all twelve known fermions -- three charged leptons, six quarks, and three neutrinos -- and the fine-structure constant $α^{-1}$, from a single discrete functional equation, the Recognition Composition Law (RCL), with \textbf{zero continuously adjustable parameters}. The mass spectrum follows from the RCL supplemented by four regularity conditions and eight structural theorems (T1--T8): the golden ratio $φ=(1+\sqrt{5})/2$ emerges as the unique hierarchy base (T6); an 8-step period is fixed by the 3-cube Hamiltonian cycle (T7); three spatial dimensions are selected by a unique combinatorial identity (T8). All integers entering the mass formula are the six combinatorial invariants of the 3-cube $Q_3$; none is fitted. The sole empirical input is the electron mass, which fixes an irreducible unit-conversion constant~$τ_0$. Predictions are confronted with PDG measurements. Charged-lepton masses are reproduced at sub-ppm accuracy for the muon and $\sim\!10^{-4}$ for the tau (Table~\ref{tab:lepton_validation}). All six quark masses are predicted at integer level; first-generation quarks agree to better than $1\%$, while second/third-generation residuals of $2$--$16\%$ are expected integer-precision effects (Table~\ref{tab:quark_validation}). Neutrino mass-squared splittings agree with NuFIT~5.3 within $1$--$2σ$, normal ordering is predicted, and $Σm_ν\approx 0.063$~eV satisfies cosmological bounds. All structural claims are machine-verified in Lean~4 (179 files, 0~\texttt{sorry}; \texttt{github.com/\allowbreak jonwashburn/\allowbreak recognition-science}).

physics.gen-ph↗

arXiv2026

Matching Rules as Cocycle Conditions: Discrete Potentials on Penrose and Canonical Projection Tilings

Aperiodic tilings support two classically studied but hitherto separately presented structures: matching rules, which enforce global order via local constraints, and height functions, which encode global geometry through integer-valued potentials. Their precise relationship has remained implicit in the literature. This paper bridges them via a cochain-first framework, establishing a four-way equivalence -- between matching rules, Ammann bar continuity, cycle closure of the associated $1$-cochains, and height-function existence -- proved for candidate tilings without presupposing any of the four conditions. The proof proceeds via a half-edge/gluing construction: for each Ammann bar family, we assign to every directed edge a signed bar-crossing count, yielding an antisymmetric $1$-cochain. A tile-side crossing function and a global cochain are built in two stages; the global cochain exists precisely when adjacent tiles agree on shared edges. Gluing implies cycle closure; the discrete Poincaré lemma then produces a scalar potential coinciding with the classical Ammann height function. The framework extends uniformly to canonical projection tilings (CPTs) from $\mathbb{Z}^N$: lattice-coordinate cochains reconstruct vertex positions via $v = \sum_{k=1}^N x_k(v)\,\mathbf{e}_k^*$, and (for CPTs with generic window) form a $\mathbb{Z}$-basis for $\check{H}^1 \cong \mathbb{Z}^N$ (Forrest--Hunton--Kellendonk), yielding a conservation-forced structure with recognition gap $\mathcal{R}(\mathcal{T}) \cong \mathbb{Z}^N$. The framework is verified for the Fibonacci chain, Penrose P2, Ammann--Beenker, and the icosahedral Ammann tiling; whether conservation forcing characterises exactly the Pisot substitution CPTs is left as an open conjecture.

math.CO↗

arXiv2025

Electric field-induced clustering in nanocomposite films of highly polarizable inclusions

A nanocomposite film containing highly polarizable inclusions in a fluid background is explored when an external electric field is applied perpendicular to the planar film. For small electric fields, the induced dipole moments of the inclusions are all polarized in field direction, resulting in a mutual repulsion between the inclusions. Here we show that this becomes qualitatively different for high fields: the total system self-organizes into a state which contains both polarizations, parallel and antiparallel to the external field such that a fraction of the inclusions is counter-polarized to the electric field direction. We attribute this unexpected counter-polarization to the presence of neighboring dipoles which are highly polarized and locally revert the direction of the total electric field. Since dipoles with opposite moments are attractive, the system shows a wealth of novel equilibrium structures for varied inclusion density and electric field strength. These include fluids and solids with homogeneous polarizations as well as equilibrium clusters and demixed states with two different polarization signatures. Based on computer simulations of a linearized polarization model, our results can guide the control of nanocomposites for various applications, including sensing external fields, directing light within plasmonic materials, and controlling the functionality of biological membranes.

cond-mat.soft↗

arXiv2025

Nonlinear ferroelectric characteristics of barium titanate nanocrystals determined via a polymer nanocomposite approach

The growing demand for high energy storage materials has garnered substantial attention towards lead-free ferroelectric nanocrystals (NCs), such as BaTiO3 (BTO), for next-generation multilayer ceramic capacitors. Notably, it remains challenging to accurately measure the dielectric constant and polarization-electric field (P-E) hysteresis loop for BTO NCs. Herein, we report on nonlinear ferroelectric characteristics of BTO NCs via a polymer nanocomposite approach. Specifically, poly(vinyl pyrrolidone)(PVP)/BTO nanocomposite films of 3-10 μm thickness, containing 380 nm tetragonal-phased and 60 nm cubic-phased BTO NCs with uniform particle dispersion, were prepared. Theoretical deconvolution of the broad experimental P-E loops of the PVP/BTO NC composite films revealed three contributions, that is, the linear deformational polarization of the nanocomposites, the polarization of BTO NCs (Pp ), and the polarization from strong particle-particle interactions. Using different mixing rules and nonlinear dielectric analysis, the overall dielectric constants of BTO NCs were obtained, from which the internal field in the BTO NCs (Ep ) was estimated. Consequently, the Pp-Ep hysteresis loops were obtained for the BTO380 and BTO60 NCs. Interestingly, BTO380 exhibited square-shaped ferroelectric loops, whereas BTO60 displayed slim paraelectric loops. This work presents a robust and versatile route to extract the Pp-Ep loops of ferroelectric NCs from polymer/ceramic nanocomposites.

cond-mat.mtrl-sci↗

arXiv2025

Challenges and opportunities in piezoelectric polymers: Effect of oriented amorphous fraction in ferroelectric semicrystalline polymers

Despite extensive research on piezoelectric polymers since the discovery of piezoelectric poly(vinylidene fluoride) (PVDF) in 1969, the fundamental physics of polymer piezoelectricity has remained elusive. Based on the classic principle of piezoelectricity, polymer piezoelectricity should originate from the polar crystalline phase. Surprisingly, the crystal contribution to the piezoelectric strain coefficient d31 is determined to be less than 10%, primarily owing to the difficulty in changing the molecular bond lengths and bond angles. Instead, >85% contribution is from Poisson's ratio, which is closely related to the oriented amorphous fraction (OAF) in uniaxially stretched films of semicrystalline ferroelectric (FE) polymers. In this perspective, the semicrystalline structure-piezoelectric property relationship is revealed using PVDF-based FE polymers as a model system. In melt-processed FE polymers, the OAF is often present and links the crystalline lamellae to the isotropic amorphous fraction. Molecular dynamics simulations demonstrate that the electrostrictive conformation transformation of the OAF chains induces a polarization change upon the application of either a stress (the direct piezoelectric effect) or an electric field (the converse piezoelectric effect). Meanwhile, relaxor-like secondary crystals in OAF (SCOAF), which are favored to grow in the extended-chain crystal (ECC) structure, can further enhance the piezoelectricity. However, the ECC structure is difficult to achieve in PVDF homopolymers without high-pressure crystallization. We have discovered that high-power ultrasonication can effectively induce SCOAF in PVDF homopolymers to improve its piezoelectric performance. Finally, we envision that the electrostrictive OAF mechanism should also be applicable for other FE polymers such as odd-numbered nylons and piezoelectric biopolymers.

cond-mat.mtrl-sci↗

arXiv2025

Ab initio calculation of electronic band structure of Cd$_{1-x}$Fe$_x$Se

The purpose of this work was to calculate the electronic band structure of Cd$_{1-x}$Fe$_x$Se. Ab-initio, calculations are performed in the Atomistix Toolkit program within the Density Functional Theory and Local Spin Density Approximation on Tight Tiger basis. We have used Hubbard U potential $U_{Fe} = 2.42$eV for 3d states for Fe ions. Super-cells of 8 and 64 atoms were constructed. After the construction of Cd$_{1-x}$Fe$_x$Se ($x=$ 6.25%; 25%) super-cells, atom relaxation and optimization of the crystal structure were carried out. Electronic band structure,and density of states were calculated, and total energy have been defined in antiferromagnetic and ferromagnetic phases. The band gap for the Cd$_{1-x}$Fe$_x$Se, $x=0.06$ in ferromagnetic phase is equal to $E_g=1.77$ eV, in antiferromagnetic phase $E_g=1.78$ eV. For $x=0.25$, $E_g=1.92$ eV. Antiferromagnetic phase considered more stable. Our calculations show that the band gap increases with the increases in Fe ion concentration.

cond-mat.mtrl-sci↗

arXiv2022

Structural correlations and phase separation in binary mixtures of charged and uncharged colloids

Structural correlations between colloids in a binary mixture of charged and uncharged spheres are calculated using computer simulations of the primitive model with explicit microions. For aqueous suspensions in a solvent of large dielectric constant, the traditional Derjaguin-Landau-Vervey-Overbeek (DLVO) theory of linear screening, supplemented with hard core interactions, reproduces the structural correlations obtained in the full primitive model quantitatively. However for lower dielectric contrast, the increasing Coulomb coupling between the micro- and macroions results in strong deviations. We find a fluid-fluid phase separation into two regions either rich in charged or rich in uncharged particles which is not reproduced by DLVO theory. Our results are verifiable in scattering or real-space experiments on charged-uncharged mixtures of colloids or nanoparticles.

cond-mat.soft↗

arXiv2022

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles

cond-mat.soft↗

arXiv2019

Crystallization seeds favour crystallization only during initial growth

Crystallization represents the prime example of a disorder order transition. In realistic situations, however, container walls and impurities are frequently present and hence crystallization is heterogeneously seeded. Rarely the seeds are perfectly compatible with the thermodynamically favoured crystal structure and thus induce elastic distortions, which impede further crystal growth. Here we use a colloidal model system, which not only allows us to quantitatively control the induced distortions but also to visualize and follow heterogeneous crystallization with single-particle resolution. We determine the sequence of intermediate structures by confocal microscopy and computer simulations, and develop a theoretical model that describes our findings. The crystallite first grows on the seed but then, on reaching a critical size, detaches from the seed. The detached and relaxed crystallite continues to grow, except close to the seed, which now prevents crystallization. Hence, crystallization seeds facilitate crystallization only during initial growth and then act as impurities.

cond-mat.soft↗

arXiv2018

Length segregation in mixtures of spherocylinders induced by imposed topological defects

We explore length segregation in binary mixtures of spherocylinders of lengths $L_1$ and $L_2$ with the same diameter $D$ which are tangentially confined on a spherical surface of radius $R$. The orientation of spherocylinders is constrained along an externally imposed direction field on the sphere which is either along the longitude or the latitude lines of the sphere. In both situations, integer orientational defects at the poles are imposed. We show that these topological defects induce a complex segregation picture also depending on the length ratio factor $γ$=$L_2/L_1$ and the total packing fraction $η$ of the spherocylinders. When the binary mixture is aligned along longitudinal lines of the sphere, shorter rods tend to accumulate at the topological defects of the polar caps whereas longer rods occupy central equatorial area of the spherical surface. In the reverse case of latitude ordering, a state can emerge where longer rods are predominantly both in the cap and in the equatorial areas and shorter rods are localized in between. As a reference situation, we consider a defect-free situation in the flat plane and do not find any length segregation there at similar $γ$ and $η$, hence the segregation is purely induced by the imposed topological defects. It is also revealed that the shorter rods at $γ$=4 and $η\ge$0.5 act as obstacles to the rotational relaxation of the longer rods when all orientational constraints are released.

cond-mat.soft↗

arXiv2017

Simulation Study of Ion Diffusion in Charged Nanopores with Anchored Terminal Groups

We present coarse-grained simulation results for enhanced ion diffusion in a charged nanopore grafted with ionomer sidechains. The pore surface is hydrophobic and its diameter is varied from 2.0 nm to 3.7 nm. The sidechains have from 2 to 16 monomers (united atom units) and contain sulfonate terminal groups. Our simulation results indicate a strong dependence of the ion diffusion along the pore axis on the pore parameters. In the case of short sidechains and large pores the ions mostly occupy the pore wall area, where their distribution is strongly disturbed by their host sulfonates. In the case of short sidechains and narrow pores, the mobility of ions is strongly affected by the structuring and polarization effects of the water molecules. In the case of long sidechains, and when the sidechain sulfonates reach the pore center, a radial charge separation occurs in the pore. Such charge separation suppresses the ion diffusion along the pore axis. An enhanced ion diffusion was found in the pores grafted with medium-size sidechains provided that the ions do not enter the central pore area, and the water is less structured around the ions and sulfonates. In this case, the 3D density of the ions has a hollow-cylinder type shape with a smooth and uninterrupted surface. We found that the maximal ion diffusion has a linear dependence on the number of sidechain monomers. It is suggested that the maximal ion diffusion along the pore axis is attained if the effective length of the sidechain extension into the pore center (measured as twice the gyration radius of the sidechain with the Flory exponent 1/4) is about 1/3 of the pore radius.

cond-mat.soft↗

arXiv2014

Magnetomechanical response of bilayered magnetic elastomers

Magnetic elastomers are appealing materials from an application point of view: they combine the mechanical softness and deformability of polymeric substances with the addressability by external magnetic fields. In this way, mechanical deformations can be reversibly induced and elastic moduli can be reversibly adjusted from outside. So far, mainly the behavior of single-component magnetic elastomers and ferrogels has been studied. Here, we go one step further and analyze the magnetoelastic response of a bilayered material composed of two different magnetic elastomers. It turns out that, under appropriate conditions, the bilayered magnetic elastomer can show a strongly amplified deformational response in comparison to a single-component material. Furthermore, a qualitatively opposite response can be obtained, i.e.\ a contraction along the magnetic field direction (as opposed to an elongation in the single-component case). We hope that our results will further stimulate experimental and theoretical investigations directly on bilayered magnetic elastomers, or, in a further hierarchical step, on bilayered units embedded in yet another polymeric matrix.

cond-mat.soft↗

arXiv2013

Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions

The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model, all ions are approximated as non-overlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman [J. Comput. Phys., 29, 35 (1978)], with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting in efficient sampling of pair-correlation functions for highly asymmetric ionic mixtures. For three-dimensional fluids, ion size- and charge-ratios larger than one thousand can be treated, corresponding to hitherto computationally not accessed micrometer-sized colloidal spheres in 1-1 electrolyte. Effective colloidal charge numbers are extracted from our primitive model results. For moderately large ion size- and charge-asymmetries, we present Molecular Dynamics simulation results that agree well with the approximate HNC pair correlations.

cond-mat.soft↗