基态非简并聚合物中的极化子和双极化子的动力学(Ⅰ)--弱电场下研究

文中模拟了在基态非简并聚合物中的极化子和双极化子在弱电场中的运动,研究了在不同简并参数的系统中极化子和双极化子的动力学稳定性,发现在同一个系统中,双极化子比极化子的运动速度慢,晶格振荡小; 在简并参数大的系统中,极化子和双极化子的运动速度都变慢.极化子和双极化子在弱电场下都存在饱和速度,达到饱和速度后, 电场的能量发生了转换.     

基态非简并聚合物中的极化子和双极化子的动力学(Ⅱ)--强电场下研究

本文模拟了基态非简并聚合物中的极化子和双极化子在强电场中的运动 ,研究了在不同简并参数的系统中极化子和双极化子的动力学稳定性,发现在强场下简并参数对极化子的稳定性影响不大,极化子晶格畸变的运动滞后于电子的运动,价带上的电子在强电场的激发下参与导电.双极化子在简并参数大的系统中较为稳定.     

Formulation and solution of the classical seashell problem

Summary Unlike its predecessor this second paper formulates the problem of seashell geometry entirely in real spaceE ³, presenting those equations of most use for parctical digital computer similations. The mathematics dilates previously mentioned clockspring “wires” (growth trajectoriesY(ϕ)) into tubular spiral surfacesr(σ, ϕ) complete with orthoclinal growth lines and simple periodic corrugations or flaresQ(σ, ϕ). It is seen that second-order theory requires a new boundary condition, the famous HLOR growth vectorr(σ, 0), which is absent from classical analyses. Thus it is demonstrated that simple periodic surface features, of a kind occurring widely in nature, obey precise Cauchy boundary conditions which may be related to the quantized cyclicities of metabolic, and geophysical, rhythms associated with biological shell growth.

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Riassunto A differenza del precedente quest'articolo formula il problema della geometria delle conchiglie completamente in spazio realeE ³, quindi presentando quelle equazioni piú utili nella simulazione pratica del computer numerico. In questa discussione i “fili” elastici a molla d'orologio (traiettorie di crescitaY(ϕ)) sono dilatari quindi diventano superfici a spirale tubolarer(σ, ϕ) e completi di anelli ortoclinati (orientati perpendicolari alla direzione di crescita) e onduleQ(σ, ϕ) periodiche semplici. Si vede che nella teoria di secondo ordine è richiesta una condizione di confine nuova, il ben conosciuto HLOR vettore di crescitar(σ, ϕ), che è assente nell'analisi classica. Quindi è dimostrato che le caratteristiche periodiche semplici delle superfici, simili a quelle molto frequenti in natura, obbediscono a precise condizioni di confine di Cauchy le quali possono essere collegate con ciclicità pulsanti di ritmi metabolici e geofisici associati con la crescita biologica delle conchiglie.

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Резюме В отличие от первой части в этатье формулируется проблема геометрии морской раковины полностью в реальном пространствеE ³, с целью получения уравнений, удобных для практического компьютерного моделирования. Математический аппарат позволяет растянуть ранее предложенные растущие траекторииT(ϕ) в цилиндрические поверхностиr(σ, ϕ), которые заканчиваются ортоклинными растущими линиями и простыми периодическими складками или раструбамиQ(σ, ϕ). Отмечается, что теория второго порядка требует нового граничного условия, известного HLOR вектораr(σ, 0), который отсутствует в классическом анализе. Показывается, что характеристики простых периодических поверхностей, широко встречающихся в природе, подчиняются граничным условиям Коши, котрые могут быть связаны с квантованными цикличностями метаболических и геофизических ритмов, связанныу с ростом биологических раковин.

     

Formulation and solution of the classical seashell problem

Summary Despite an extensive scholarly literature dating back to classical times, seashell geometries have hitherto resisted rigorous theoretical analysis, leaving applied scientists to adopt a directionless empirical approach toward classification. The voluminousness of recent palaeontological literature demonstrates the importance of this problem to applied scientists, but in no way reflects corresponding conceptual or theoretical advances beyond the XIX century thinking which was so ably summarized by Sir D’Arcy Wentworh Thompson in 1917. However, in this foundation paper for the newly emerging science of theoretical conchology, unifying theoretical considerations for the first time, permits a rigorous formulation and a complete solution of the problem of biological shell geometries. Shell coilingabout the axis of symmetry can be deduced from first principles using energy considerations associated with incremental growth. The present paper shows that those shell apertures which are incurved (?cowrielike?), outflared (?stromblike?) or even backturned (?Opisthostomoidal?) are merely special cases of a much broader spectrum of ?allowable? energy-efficient growth trajectories (tensile elastic clockspring spirals), many of which were widely used by Cretaceous ammonites. Energy considerations also dictate shell growthalong the axis of symmetry, thus seashell spires can be understood in terms of certain special figures of revolution (M?bius elastic conoids), the better-known coeloconoidal and cyrtoconoidal shell spires being only two special cases arising from a whole class of topologically possible, energy efficient and biologically observed geometries. The ?wires? and ?conoids? of the present paper are instructive conceptual simplifications sufficient for present purposes. A second paper will later deal with generalized tubular surfaces in three dimensions.

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Riassunto Malgrado un’ampia e dotta letteratura che risale ai tempi classici, la geometria delle conchiglie ha resistito fino ad ora ad analisi teoriche rigorose, quindi gli scienziati che si cimentano in questo campo hanno adottato un metodo empirico senza direttiva per quanto riguarda la classificazione. L’abbondanza della recente letteratura paleontologica dimostra l’importanza di questo problema per gli scienziati di questo campo, ma non riflette in alcun modo i corrispondenti progressi concettuali o teorici rispetto al pensiero del diciannovesimo secolo che venne cosí abilmente riassunto da Sir D’Arcy Wentworth Thompson nel 1917. Tuttavia, in questo lavoro fondamentale per la nuova scienza emergente di conchigliologia teorica, l’unificazione delle considerazioni teoriche permette una rigorosa formulazione e una completa soluzione del problema della geometria biologica delle conchiglie. L’avvolgimento delle conchiglieintorno all’asse di simmetria si deduce dai primi princípi usando considerazioni sull’energia associata alla crescita per aumento di dimensioni. Questo lavoro mostra che le aperture delle conchiglie che sono incurvate (di tipo ?cowrie?), allargate verso l’esterno (di tipo ?strombe?) o anche rivoltate all’indietro (di tipo ?opistostomoideo?) sono solamente casi speciali di uno spettro piú ampio di traiettorie di crescita efficienti d’energia ?permesse? (spirali tensili, elastiche a molla d’orologio), molte delle quali vennero estesamente usate dagli ammoniti del Cretaceo. Considerazioni d’energia dettano anche la crescita della conchiglialungo l’asse di simmetria, cosí le spirali delle conchiglie marine possono essere comprese nei termini di certe speciali figure di rivoluzione (conoidi elastici di M?bius), essendo i gusci meglio conosciuti delle conchiglie coeloconoidali e cyrtoconoidali soltanto due casi speciali che derivano da una intera classe di geometria topologicamente possibili, efficienti di energia e biologicamente osservate. I ?fili? e i ?conoidi? di questo lavoro sono istruttive semplificazioni concettuali sufficienti a questo scopo. Un secondo lavoro tratterà successivamente superfici tubolari generalizzate in tre dimensioni.

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Резюме Несмотря на большое количество литературы, до настоящего времени отсутствует строгий теоретический анализ геометрией морских раковин. Многотомность существующей палеонтологической литературы демонстрирует важность этой проблемы для прикладных ученых ине отражает соответствующих концептуальных и теоретических достижений после XIX века, которые были систематизированы Томсоном в 1917 г. Однако в этой фундаментальной работе по теоретической конхиологии были объединены теоретические рассмотрения, которые впервые позволили сформулировать и полностью решить проблему биологических геометрий морских раковин. Свертывание раковин спиралью вокруг оси симметрии можно получить из первых принципов, используя энергетические рассуждения, связанные с дифференциальным ростом. В настоящей статье показывается, что те отверстия раковин, которые являются искривленными, в форме раструба, или даже повернутыми назад, представляют просто частные случаи более широкого спектра ?разрешенных? траекторий роста. Энергетические рассуждения ткаже диктуют рост раковин вдоль оси симметрии, тонкое острие морских раковин можно понять в терминах некоторых специальных фигур вращения. ?Провода? и ?коноиды? настоящей статьи представляют поучительные концептуальные упрощения, достаточные для наших целей. Вторая статья будет посвящена трубчатым поверхностям в трех измерениях.

     

The virial theorem and the ground state problem in polaron theory

The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong-coupling polaron (the Pekar 1: 2: 3: 4 theorem).     

The impedance function of a confined polaron and bipolaron: The single-path-integral approach

We use the single-path-integral to calculate the impedance function of the polaron and bipolaron in quantum confinement with the presence of the external fields. The expectation values of the classical equation of motion is considered in order to obtain the impedance function. The mobility of the polaron and bipolaron in quantum confinement is also calculated in the direction parallel and perpendicular to the magnetic field. Without trapping, we also calculate the effective mass of the bipolaron in the magnetic field.     

On the classical solution of SO(3) gauge theory and ’t Hooft-Polyakov monopole

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.     

Breakdown of classical nucleation theory near isostructural phase transitions

We report simulations of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model. We argue that the observed behavior is due to the surface stress of the crystal nuclei. The observed effect highlights a general deficiency of the most frequently used thermodynamic theories for crystal nucleation. Surface stress should lead to an experimentally observable expansion of crystal nuclei of colloids with short-ranged attraction and of globular proteins.     

The Hartree-Fock and Generator Coordinate Methods in field theory. The polaron problem

Well known results of the strong coupling theory of the polaron are derived by simple variational methods (The Hartree-Fock and the Generator Coordinate Methods) based on coherent-state-wave-functions describing the electron surrounded by a phonon cloud.     

M theory solution to the hierarchy problem

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2 holonomy without fluxes. This gives stable vacua with softly broken supersymmetry, grand unification, and a distinctive spectrum of TeV and sub-TeV sparticle masses.     

共轭高分子链中极化子间相互作用对电荷迁移率的影响

基于综合考虑了电子与声子以及电子与电子相互作用的理论模型,采用数值方法计算了在外电场作用下共轭高聚物分子中电荷的迁移率,讨论了大小极化子共存并相互作用对分子链内电荷迁移率的影响。研究发现,电荷迁移率明显受大小极化子的载荷性质的影响,当大小极化子具有相同电性时,在低电场范围内,分子内电荷迁移率由大极化子运动性质主导,而在高电场范围内,分子内电荷迁移率由小极化子主导;另一方面,当大小极化子具有相反电性时,电荷迁移率只由大极化子运动性质主导,与电场强度无关。此外,还讨论了电子与电子相互作用对电荷迁移率"的影响。     

On the general form of the Beltrami equation and Papkovich's solution of the axially symmetrical problem of the classical theory of elasticity

The paper shows the connection between the general form of the Beltrami equation of compatibility, which had already been derived by the author, and the form given for it in orthogonal curvilinear coordinates by Lurye (para 2, 3).Some of the properties of Papkovich's general solution of the axially symmetrical problem (without body forces) of the theory of elasticity and its relation to the Finzi-Krutkov solution are discussed so as to supplement to a certain extent the paper of Trenin (para 4, 5, 6).     

The gauge fixing problem around classical solutions of the Yang-Mills theory

We show that the Gribov problem [1] does not exist for small deformations of an irreducible gauge potential, in the covariant background gauge. This justifies gauge fixing within the framework of perturbation expansion. In proving the existence of local gauge sections we investigate the global orbit structure around an irreducible gauge potential.     

One solution of the problem of intrinsic energy of a point charge,as obtained within classical relativistic field theory

New equations are proposed for classical relativistic field theory, which insure a finite value for the intrinsic energy of a point charge.Mechanics and Physics Scientific Research Institute, Saratov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 26–30, October, 1994.     

Resolution of the out-of-zone solution problem in envelope-function theory

Envelope-function equations are widely used to model electron states in microstructures where single-band effective mass models are inappropriate. However, the presence of spurious out-of-zone solutions poses a serious problem for the method: the out-of-zone solutions appear unphysical yet including them is necessary to satisfy all the boundary conditions implied by the envelope-function equations. In an earlier publication, the author has suggested that the mathematically correct procedure is to use all solutions, including out-of-zone solutions, of the envelope-function equations and to apply all the boundary conditions implied by those equations at abrupt interfaces. This procedure is applied to a simple one-dimensional model and it is shown that it generates the correct wavefunction and the role of the out-of-zone solutions is clarified. As a result of this work there is now a straightforward unambiguous procedure for applying the envelope-function method to microstructures, a procedure that removes uncertainty, but retains the simplicity of the envelope-function\break approach.     

Analysis of dichroism and torque data in YIG (Si) in terms of small polaron theory

An analysis of photoinduced dichroism and torque data in YIG (Si) is made in terms of a small polaron model. Good agreement between theory and experiment is found for the frequency — and angular dependence of the effects if the distortions of the lattice due to the silicon doping are treated semiempirically. To understand the absolute magnitude of the effects one is forced to assume that only one fifth of the carriers are immobile at low temperatures in agreement with results by Teale.     

Quantum meaning of classical (field) theory for fermi systems

We investigate the cosmological consequences of a phase transition which is driven primarily by slow nucleation of bubbles of the new phase via the effectively zero temperature quantum tunneling process of Coleman and Callan. These bubbles will asymptotically fill an arbitrarily large fraction of the space, yet they never percolate. Instead they form finite clusters, with each cluster dominated by a single largest bubble. The large scale thermalization required by the original “inflationary universe” scenario does not take place. The Coleman-De Luccia formalism for bubble formation in curved space is reviewed, with minor extensions. We argue that a single uncollided bubble would contain much less total entropy than the observed universe, unless the Higgs field potential involves widely disparate mass scales, as in the new inflationary universe scenario. We also argue that finite clusters are unlikely to yield a homogeneous and isotropic region containing sufficient entropy. Thus, unless the Higgs potential has the special form required by the new inflationary scenario, it appears quite implausible that there was such a phase transition in our past.