INFLUENCE OF THE SIZE EFFECT ON THE REGULARITIES OF THE STRUCTURE FORMATION IN BIMETALLIC Au-Co NANOPARTICLES

В данной работе методом молекулярной динамики с использованием потенциала сильной связи исследовались биметаллические наночастицы Au - Co трёх стехиометрических составов различного размера. Установлены закономерности структурообразования, описаны их характерные особенности. В частности, в составах с 50ат.% и 75ат.% содержанием Au образуются множественные малые ядра локальной икосаэдрической симметрии. Только в составе Co -25ат.% Au с увеличением размера частиц преобладают кристаллические фазы. Выявлены составы, в которых внутренняя симметрия наночастицы определена наличием одного икосаэдра, либо сверхструктуры из нескольких икосаэдров. Рассчитаны концентрационные зависимости энергии смешения биметаллической наночастицы Au - Co. Показано, что в определённом диапазоне размеров существуют концентрационные составы, при которых биметаллический наносплав может проявлять нестабильность. С использованием калорических кривых потенциальной части внутренней энергии определены температуры кристаллизации. Установлено, что температура кристаллизации демонстрирует умеренный, либо существенный, в зависимости от состава, рост с увеличением размера биметаллических наночастиц Au - Co. This work studied bimetallic Au - Co nanoparticles of three stoichiometric compositions of various sizes by the molecular dynamics method using the tight-binding potential. The regularities of structure formation are established, their characteristic features are described. In particular, in compositions with 50at% and 75at% Au content, multiple small nuclei of local icosahedral symmetry are formed. Crystalline phases prevail only in the Co - 25 at% Au composition with an increase in the particle size. Compositions are revealed in which the internal symmetry of a nanoparticle is determined by the presence of one icosahedron or a superstructure of several icosahedrons. The concentration dependences of the mixing energy of a bimetallic Au - Co nanoparticle are calculated. It is shown that there are concentrations of compositions at which bimetallic nanoalloys can exhibit instability in a certain size range. Crystallization temperatures were determined using the caloric curves of the potential part of the internal energy. It was found that the crystallization temperature demonstrates a moderate or significant, depending on the composition as well as growth with an increase in the size of bimetallic Au - Co nanoparticles.

New Symmetries, Conserved Quantities and Gauge Nature of a Free Dirac Field

We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein–Gordon equation (KGE). We demonstrate that all the solutions to the DE (possessing point- or string-like singularities) can be obtained via differentiation of a corresponding pair of the KGE solutions for a doublet of scalar fields. In this way, we obtain a “spinor analogue” of the mesonic Yukawa potential and previously unknown chains of solutions to DE and KGE, as well as an exceptional solution to the KGE and DE with a finite value of the field charge (“localized” de Broglie wave). The pair of scalar “potentials” is defined up to a gauge transformation under which corresponding solution of the DE remains invariant. Under transformations of Lorentz group, canonical spinor transformations form only a subclass of a more general class of transformations of the solutions to DE upon which the generating scalar potentials undergo transformations of internal symmetry intermixing their components. Under continuous turn by one complete revolution the transforming solutions, as a rule, return back to their initial values (“spinor two-valuedness” is absent). With an arbitrary solution of the DE, one can associate, apart from the standard one, a non-canonical set of conserved quantities, positive definite “energy” density among them, and with any KGE solution-positive definite “probability density”, etc. Finally, we discuss a generalization of the proposed procedure to the case when the external electromagnetic field is present.

Mirror channel eigenvectors of the d-dimensional fishnets

We present a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in d-dimensions. The eigenvectors of a fishnet lattice of length N depend on a set of N quantum numbers (uk, lk ), each associated with the rapidity and bound-state index of a lattice excitation. Each excitation is a particle in (1 + 1)-dimensions with O(d) internal symmetry, and the wave-functions are formally constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra. These properties are proved via the representation, new to our knowledge, of the matrix elements of the fused R-matrix with O(d) symmetry as integral operators on the functions of two spacetime points. The spectral decomposition of a fishnet integral we achieved can be applied to the computation of Basso-Dixon integrals in higher dimensions.

Multivector Fields of Noether Symmetries in the Lagrangian Formalism and Belinfante Tensor

Elsewhere, we gave the explicit expressions of the multivectors fields associated to infinitesimal symmetries which gave rise to Noether currents for classical field theories and relativistic mechanic using the Second Order Partial Differential Equation SOPDE condition for the Poincar\'e-Cartan form.\\ The main objective of this paper is to reformulate the multivector fields associated to translational and rotational symmetries of the gauge fields in particular those of the electromagnetic field which gave rise to symmetrical and invariant gauge energy-momentum tensor and the orbital angular momentum. The spin angular momentum appears however because of the internal symmetry inside the fiber.

Addendum: Hidden symmetries, trivial conservation laws and Casimir invariants in geophysical fluid dynamics (2018 J. Phys. Commun. 2 115018)

An extension is proposed to the internal symmetry transformations associated with mass, entropy and other Clebsch-related conservation in geophysical fluid dynamics. Those symmetry transformations were previously parameterized with an arbitrary function  of materially conserved Clebsch potentials. The extension consists in adding potential vorticity q to the list of fields on which a new arbitrary function  depends. If  = q  ( s ) , where  ( s ) is an arbitrary function of specific entropy s, then the symmetry is trivial and gives rise to a trivial conservation law. Otherwise, the symmetry is non-trivial and an associated non-trivial conservation law exists. Moreover, the notions of trivial and non-trivial Casimir invariants are defined. All non-trivial symmetries that become hidden following a reduction of phase space are associated with non-trivial Casimir invariants of a non-canonical Hamiltonian formulation for fluids, while all trivial conservation laws are associated with trivial Casimir invariants.

Hexagonalization of Fishnet integrals. Part I. Mirror excitations

In this paper we consider a conformal invariant chain of L sites in the unitary irreducible representations of the group SO(1, 5). The k-th site of the chain is defined by a scaling dimension ∆k and spin numbers $$ \frac{\ell_k}{2},\frac{\ell_k}{2} $$ ℓ k 2 , ℓ k 2 The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice “fishnet” integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the mirror excitations of the lattice: particles with SO(4) internal symmetry that scatter according to an integrable factorized $$ \mathcal{S} $$ S -matrix in (1 + 1) dimensions

Spontaneously Broken Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

Gauge Interactions

The principle of gauge symmetry is introduced as a consequence of the invariance of the equations of motion under local transformations. We apply it to Abelian, as well as non-Abelian, internal symmetry groups. We derive in this way the Lagrangian of quantum electrodynamics and that of Yang–Mills theories. We quantise the latter using the path integral method and show the need for unphysical Faddeev–Popov ghost fields. We exhibit the geometric properties of the theory by formulating it on a discrete space-time lattice. We show that matter fields live on lattice sites and gauge fields on oriented lattice links. The Yang–Mills field strength is related to the curvature in field space.

Modeling and Structure Determination of Homo-Oligomeric Proteins: An Overview of Challenges and Current Approaches

Protein homo-oligomerization is a very common phenomenon, and approximately half of proteins form homo-oligomeric assemblies composed of identical subunits. The vast majority of such assemblies possess internal symmetry which can be either exploited to help or poses challenges during structure determination. Moreover, aspects of symmetry are critical in the modeling of protein homo-oligomers either by docking or by homology-based approaches. Here, we first provide a brief overview of the nature of protein homo-oligomerization. Next, we describe how the symmetry of homo-oligomers is addressed by crystallographic and non-crystallographic symmetry operations, and how biologically relevant intermolecular interactions can be deciphered from the ordered array of molecules within protein crystals. Additionally, we describe the most important aspects of protein homo-oligomerization in structure determination by NMR. Finally, we give an overview of approaches aimed at modeling homo-oligomers using computational methods that specifically address their internal symmetry and allow the incorporation of other experimental data as spatial restraints to achieve higher model reliability.