Exact Analogue Research Articles

Molecular thermodynamics of a quantum Lennard-Jones fluid using an effective Mie potential and the SAFT-VR-Mie approach

The SAFT-VR-Mie approach is applied to model quantum fluids following a method presented previously on the combined use of thermodynamic perturbation theory (TPT) and path-integral Monte Carlo (PIMC) simulations to describe a quantum square-well (QSW) fluid. In this communication we consider a system of N particles contained within a volume V interacting via a quantum Lennard-Jones potential (QLJ) with de Broglie's thermal wavelength , where m denotes the particle's mass, T is the temperature and h and k are the Planck's and Boltzmann's constants, respectively. The method is based on the exact analogy between the discretised path-integral formalism of Quantum Mechanics and the partition function of a classical system composed of necklace molecules. The Zwanzig's expansion is implemented in order to obtain the QLJ's first-perturbation term, , from PIMC simulations. An effective Mie potential with a variable repulsive parameter range and fixed attractive parameter, , is obtained by mapping to the classical expression provided by the SAFT-VR-Mie value, . The thermodynamics of the QLJ system is obtained using the SAFT-VR-Mie equation of state and applied to obtain accurate predictions for molecular hydrogen's isotherms when .

Thalhammerite, Pd9Ag2Bi2S4, a New Mineral from the Talnakh and Oktyabrsk Deposits, Noril’sk Region, Russia

Thalhammerite, Pd9Ag2Bi2S4, is a new sulphide discovered in galena-pyrite-chalcopyrite and millerite-bornite-chalcopyrite vein-disseminated ores from the Komsomolsky mine of the Talnakh and Oktyabrsk deposits, Noril’sk region, Russia. It forms tiny inclusions (from a few μm up to about 40–50 μm) intergrown in galena, chalcopyrite, and also in bornite. Thalhammerite is brittle and has a metallic lustre. In plane-polarized light, thalhammerite is light yellow with weak bireflectance, weak pleochroism, in shades of slightly yellowish brown and weak anisotropy; it exhibits no internal reflections. Reflectance values of thalhammerite in air (R1, R2 in %) are: 41.9/43.0 at 470 nm, 43.9/45.1 at 546 nm, 44.9/46.1 at 589 nm, and 46.3/47.5 at 650 nm. Three spot analyses of thalhammerite give an average composition: Pd 52.61, Bi 22.21, Pb 3.92, Ag 14.37, S 7.69, and Se 0.10, total 100.90 wt %, corresponding to the empirical formula Pd8.46Ag2.28(Bi1.82Pb0.32)Σ2.14(S4.10Se0.02)Σ4.12 based on 17 atoms; the average of five analyses on synthetic thalhammerite is: Pd 55.10, Bi 24.99, Ag 12.75, and S 7.46, total 100.30 wt %, corresponding to Pd8.91Ag2.03Bi2.06S4.00. The density, calculated on the basis of the empirical formula, is 9.72 g/cm3. The mineral is tetragonal, space group I4/mmm, with a 8.0266(2), c 9.1531(2) Å, V 589.70(2) Å3 and Z = 2. The crystal structure was solved and refined from the single-crystal X-ray-diffraction data of synthetic Pd9Ag2Bi2S4. Thalhammerite has no exact structural analogues known in the mineral system; chemically, it is close to coldwellite (Pd3Ag2S) and kravtsovite (PdAg2S). The strongest lines in the X-ray powder diffraction pattern of synthetic thalhammerite [d in Å (I) (hkl)] are: 3.3428(24)(211), 2.8393(46)(220), 2.5685(21)(301), 2.4122(100)(222), 2.3245(61)(123), 2.2873(48)(004), 2.2201(29)(132), 2.0072(40)(400), 1.7481(23)(332), and 1.5085(30)(404). The mineral honours Associate Professor Oskar Thalhammer of the University of Leoben, Austria.

Vectorial nonlinear potential theory

We settle the longstanding problem of establishing pointwise potential estimates for vectorial solutions u\colon \Omega \to \mathbb R^{N} to the non-homogeneous p -Laplacean system -\mathrm{div} (|Du|^{p-2}Du)=\mu \qquad \text{in}\ \Omega \subset \mathbb R^{n}\,, where \mu is a \mathbb R^{N} -valued measure with finite total mass. In particular, for solutions u \in W^{1,1}(\mathbb R^{n}) , the global estimates via Riesz and Wolff potentials |Du(x_0)|^{p-1} \lesssim \int_{\mathbb R^{n}}\frac{d|\mu|(x)}{|x-x_0|^{n-1}} and |u(x_0)|\lesssim {\bf W}^{\mu}_{1, p}(x_0,\infty) = \int_0^\infty \left(\frac{|\mu|(B_\varrho(x_0))}{\varrho^{n-p}}\right)^{1/(p-1)}\, \frac{d\varrho}{\varrho} respectively, hold at every point x_0 such that the corresponding potentials are finite. The estimates allow to give sharp descriptions of fine properties of solutions which are the exact analog of the ones in classical linear potential theory. For instance, sharp characterisation of Lebesgue points of u and Du and optimal regularity criteria for solutions are provided exclusively in terms of potentials.

Noise in tunneling spin current across coupled quantum spin chains

We theoretically study the spin current and its dc noise generated between two spin-1/2 spin chains weakly coupled at a single site in the presence of an over-population of spin excitations and a temperature elevation in one subsystem relative to the other, and compare the corresponding transport quantities across two weakly coupled magnetic insulators hosting magnons. In the spin chain scenario, we find that applying a temperature bias exclusively leads to a vanishing spin current and a concomitant divergence in the spin Fano factor, defined as the spin current noise-to-signal ratio. This divergence is shown to have an exact analogy to the physics of electron scattering between fractional quantum Hall edge states and not to arise in the magnon scenario. We also reveal a suppression in the spin current noise that exclusively arises in the spin chain scenario due to the fermion nature of the spin-1/2 operators. We discuss how the spin Fano factor may be extracted experimentally via the inverse spin Hall effect used extensively in spintronics.

A generalization of Schur functions: Applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks

Recent work on return properties of quantum walks (the quantum analogue of random walks) has identified their generating functions of first returns as Schur functions. This is connected with a representation of Schur functions in terms of the operators governing the evolution of quantum walks, i.e. the unitary operators on Hilbert spaces.In this paper we propose a generalization of Schur functions by extending the above operator representation to arbitrary closed operators on Banach spaces. Such generalized ‘Schur functions’ meet the formal structure of first return generating functions, thus we call them FR-functions. We derive some general properties of FR-functions, among them a simple relation with an operator version of Stieltjes functions which generalizes the renewal equation already known for random and quantum walks. We also prove that FR-functions satisfy splitting properties which extend useful factorizations of Schur functions.When specialized to self-adjoint operators on Hilbert spaces, we show that FR-functions become Nevanlinna functions. This allows us to obtain properties of Nevanlinna functions which, as far as we know, seem to be new. The FR-function structure leads to a new operator representation of Nevanlinna functions in terms of self-adjoint operators, whose spectral measures provide also new integral representations of such functions. This allows us to characterize each Nevanlinna function by a measure on the real line, which we refer to as ‘the measure of the Nevanlinna function’. In contrast to standard operator and integral representations of Nevanlinna functions, these new ones are exact analogues of those already known for Schur functions. The above results are also the source of a very simple ‘Schur algorithm’ for Nevanlinna functions based on interpolations at points on the real line, which we refer to as the ‘Schur algorithm on the real line’.The paper is completed with several applications of FR-functions to orthogonal polynomials and random and quantum walks which illustrate their wide interest: an analogue for orthogonal polynomials on the real line of the Khrushchev formula for orthogonal polynomials on the unit circle, and the use of FR-functions to study recurrence in random walks, quantum walks and open quantum walks. These applications provide numerous explicit examples of FR-functions, clarifying the meaning of these functions –as first return generating functions– and their splittings –which become recurrence splitting rules. They also show that these new tools, despite being extensions of very classical ones, play an important role in the study of physical problems of a highly topical nature.

On the pointfree counterpart of the local definition of classical continuous maps

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar classical counterpart concerning finite closed covers of a space $X$ (Picado and Pultr [4]). This note presents alternative proofs of these pointfree results which differ from those of [4] by treating the issue in terms of frame homomorphisms while the latter deals with the dual situation concerning localic maps. A notable advantage of the present approach is that it also provides proofs of the analogous results for some significant variants of frames which are not covered by the localic arguments.

Grey forest soils in the different classification systems

According to various data, the area of grey forest soils in the world is 94–120.2 million ha, in Ukraine – 4.7–5.5 million ha (about 9 % of the country’s territory). The diversity of conditions for the formation of these soils, discussions about their genesis are the causes of different approaches to the classification of grey forest soils. The history of the classification of grey forest soils is analysed; the most common variants of their classification in Ukraine are presented. Seeking to find approximate equivalents, an attempt to find grey forest soils in the classification systems of different countries (Russia, Moldova, Bulgaria, Romania, Czech Republic, Poland, USA, Canada), as well as in the legend of the FAO-UNESCO map and the WRB has been made. To establish exact analogues of soils practically it is impossible due to different principles of classification’s construction. Modern soil classifications of different countries are as close as possible to WRB and “Soil Taxonomy”. The following names of grey forest soils are identified as the most grounded: light grey forest, grey forest and dark grey podzolic. The following equivalents of the WRB nomenclature (2014) for sub-types of grey forest soils are offered: light grey forest – Albic Luvisols, grey forest – Haplic Luvisols, dark grey podzolic – Luvic Greyzemic Phaeozems. To the names of analogues of these soils with gleyic properties, the qualifier “Gleyic” should be added before the name of the reference soil group. The urgent task for soil scientists of Ukraine is to create a new soil classification that would preserve the acquisitions of genetic soil science but took into account the world trends: the allocation of diagnostic horizons and features that have clearly defined quantitative boundaries. In the new classification, it is proposed to combine the light grey and grey forest soils by a separate group, dark grey podzolic soils to be grouped together in a group with podzolic chernozems. The need for such selection is confirmed by the study of the dark grey soils position in different classification systems of the world, most of which these soils are in the chernozemic type group (Mollisols, Phaeozems and Chernozems). Key words: classification, grey forest soils, Greyzems, Luvisols, Mollisols, Phaeozems.

Exact Discretization of an Economic Accelerator and Multiplier with Memory

Fractional differential equations of macroeconomics, which allow us to take into account power-law memory effects, are considered. We describe an economic accelerator and multiplier with fading memory in the framework of discrete-time and continuous-time approaches. A relationship of the continuous- and discrete-time fractional-order equations is considered. We propose equations of the accelerator and multiplier for economic processes with power-law memory. Exact discrete analogs of these equations are suggested by using the exact fractional differences of integer and non-integer orders. Exact correspondence between the equations with finite differences and differential equations lies not so much in the limiting condition, when the step of discretization tends to zero, as in the fact that mathematical operations, which are used in these equations, satisfy in many cases the same mathematical laws.

Testing the Effectiveness of Protocols for Removal of Common Conservation Treatments for Radiocarbon Dating

AbstractTo achieve a reliable radiocarbon (14C) date for an object, any contamination that may be of a different age must be removed prior to dating. Samples that have been conserved with treatments such as adhesives, varnishes or consolidants can pose a particular challenge to14C dating. At the Oxford Radiocarbon Accelerator Unit (ORAU), common examples of such substances encountered include shellac, the acrylic polymers Paraloid B-67 and B-72, and vinyl acetate-derived polymers (e.g. PVA). Here, a non-carbon-containing absorbent substrate called Chromosorb®was deliberately contaminated with a range of varieties or brands of these conservation treatments, as well as two cellulose nitrate lacquers. A selection of chemical pretreatments was tested for their efficiency at removing them. While the varieties of shellac and Paraloid tested were completely removed with some treatments (water/methanol and acetone/methanol/chloroform sequential washes, respectively), no method was found that was capable of completely removing any of the vinyl acetate-derived materials or the cellulose nitrate lacquers. While Chromosorb is not an exact analog of archaeological wood or bone, for example, this study suggests that it may be possible to remove aged shellac and Paraloid from archaeological specimens with standard organic solvent-acid-base-acid pretreatments, but it may be significantly more difficult to remove vinyl acetate-derived polymers and cellulose nitrate lacquers sufficiently to provide reliable14C dates. The four categories of conservation treatment studied demonstrate characteristic FTIR spectra, while highlighting subtle chemical and molecular differences between different varieties of shellac, Paraloid and cellulose nitrate lacquers, and significant differences between the vinyl acetate derivatives.

A Wolff Theorem for finite rank bounded symmetric domains

We present a Wolff Theorem for all infinite dimensional bounded symmetric domains of finite rank. Namely, if B is the open unit ball of any finite rank JB⁎-triple and f:B→B is a compact holomorphic map with no fixed point in B, we prove convex f-invariant subdomains of B (of all sizes and at all points) exist in the form of simple operator balls cλ+Tλ(B), for cλ∈B and Tλ an invertible linear map. These are exact infinite dimensional analogues of the invariant discs in Δ, the invariant ellipsoids in the Hilbert ball and invariant domains in finite dimensional triples. Results are new for rank >2, even for classical spaces such as C⁎-algebras and JB⁎-algebras.

Strong Converse Exponent for Classical-Quantum Channel Coding

We determine the exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity. Our form of the exponent is an exact analogue of Arimoto’s, given as a transform of the Rényi capacities with parameters $${\alpha > 1}$$ . It is important to note that, unlike in the classical case, there are many inequivalent ways to define the Rényi divergence of states, and hence the Rényi capacities of channels. Our exponent is in terms of the Rényi capacities corresponding to a version of the Rényi divergences that has been introduced recently in Müller-Lennert et al. (J Math Phys 54(12):122203, 2013. arXiv:1306.3142 ), and Wilde et al. (Commun Math Phys 331(2):593–622, 2014. arXiv:1306.1586 ). Our result adds to the growing body of evidence that this new version is the natural definition for the purposes of strong converse problems.

3D Chiral Plasmonic Metamaterials Fabricated by Direct Laser Writing: The Twisted Omega Particle

The plasmonic version of a 3D chiral meta‐atom which consists of a loop‐wire structure, namely the so‐called twisted omega particle, is experimentally realized. The structure is fabricated by direct laser writing and subsequent electroless silver plating, a novel technique capable of producing truly 3D photonic nanostructures. In this case, the metallic wire of finite length supports an electric dipole resonance, whereas the loop acts as a split‐ring resonator which exhibits a magnetic dipole resonance, leading to the separation of right‐handed circularly polarized light and the left‐handed one. The arising optical activity is discussed in terms of a single oscillator model system used classically to describe the generation of natural optical activity in chiral media, and it is shown that the twisted omega particle acts as its exact plasmonic analogue.

Identifying the causes of the bullwhip effect by exploiting control block diagram manipulation with analogical reasoning

Senior managers when solving problems commonly use analogical reasoning, allowing a current ‘target problem’ situation to be compared to a valid previous experienced ‘source problem’ from which a potential set of ‘candidate solutions’ may be identified. We use a single-echelon of the often-quoted Forrester (1961) production-distribution system as a case ‘target model’ of a complex production and inventory control system that exhibits bullwhip. Initial analogical reasoning based on ‘surface similarity’ would presuppose a classic control engineering ‘source model’ consisting of a phase-lag feedback system for which it is difficult to derive the transfer function. Simulation alone would have to be relied on to mitigate the bullwhip effect. By using z-transform block diagram manipulation, the model for a single-echelon, consisting of 17 difference equations with five feedback loops is shown to have exact analogy to Burns and Sivazlian's (1978) second order system that has no feedback. Therefore, this more appropriate ‘source model’ is based on a deeper understanding of the ‘behavioral similarities’ which indicates that the bullwhip effect is not in the case of the ‘target model’ due to feedback control but due to a first-order derivative, ‘phase advance’, term in the feed forward numerator path. Hence a more appropriate ‘candidate solution’ can be found via the use of a ‘recovery’ filter. An interdisciplinary framework for exploiting control engineering block diagram manipulation, utilizing analogical reasoning, in a practical setting is presented, as is an example in a contemporary supply chain situation.

Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space.

Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.

Loop gravity string

In this work we study canonical gravity in finite regions for which we introduce a generalisation of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersuface with a boundary sphere and show how the presence of this term leads to an unprecedented type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a 3-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux and that the string stress tensor represents the two dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphisms charges of quantum geometry satisfy at each puncture a Virasoro algebra with central charge $c=3$. This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary $SU(2)$ gauge symmetry is recovered via the action of the $U(1)^3$ Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin-representation. We finally show that this symmetry is broken by the presence of background curvature.

Accelerators in Macroeconomics: Comparison of Discrete and Continuous Approaches

We prove that the standard discrete-time accelerator equation cannot be considered as an exact discrete analog of the continuous-time accelerator equation. This leads to fact that the standard discrete-time macroeconomic models cannot be considered as exact discretization of the corresponding continuous-time models. As a result, the equations of the continuous and standard discrete models have different solutions and can predict the different behavior of the economy. In this paper, we propose a self-consistent discrete-time description of the economic accelerators that is based on the exact finite differences. For discrete-time approach, the model equations with exact differences have the same solutions as the corresponding continuous-time models and these discrete and continuous models describe the same behavior of the economy. Using the Harrod-Domar growth model as an example, we show that equations of the continuous-time model and the suggested exact discrete model have the same solutions and these models predict the same behavior of the economy.

On the shape of giant soap bubbles

We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical size [Formula: see text], where [Formula: see text] is the mean thickness of the soap film and [Formula: see text] is the capillary length ([Formula: see text] stands for vapor-liquid surface tension, and [Formula: see text] stands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures.

The Probability Anomaly Correlation and Calibration of Probabilistic Forecasts

Abstract An ordinary regression of predicted versus observed probabilities is presented as a direct and simple procedure for minimizing the Brier score (BS) and improving the attributes diagram. The main example applies to seasonal prediction of extratropical sea surface temperature by a global coupled numerical model. In connection with this calibration procedure, the probability anomaly correlation (PAC) is developed. This emphasizes the exact analogy of PAC and minimizing BS to the widely used anomaly correlation (AC) and minimizing mean squared error in physical units.

Translation principle for Dirac index

Let $G$ be a finite cover of a closed connected transpose-stable subgroup of ${\rm GL}(n,\Bbb{R})$ with complexified Lie algebra ${\frak g}$. Let $K$ be a maximal compact subgroup of $G$, and assume that $G$ and $K$ have equal rank. We prove a translation principle for the Dirac index of virtual $({\frak g},K)$-modules. As a byproduct, to each coherent family of such modules, we attach a polynomial on the dual of the compact Cartan subalgebra of ${\frak g}$. This ``index polynomial'' generates an irreducible representation of the Weyl group contained in the coherent continuation representation. We show that the index polynomial is the exact analogue on the compact Cartan subgroup of King's character polynomial. The character polynomial was defined by King on the maximally split Cartan subgroup, and it was shown to be equal to the Goldie rank polynomial up to a scalar multiple. In the case of representations of Gelfand-Kirillov dimension at most half the dimension of $G/K$, we also conjecture an explicit relationship between our index polynomial and the multiplicities of the irreducible components occurring in the associated cycle of the corresponding coherent family.

ПЕРЕВОД (ÜBERSETZUNG) И ПЕРЕДАЧА ЗНАЧЕНИЯ (SPRACHMITTLUNG) НЕМЕЦКИХ СОЦИОЭКОЛОГИЧЕСКИХ ТЕРМИНОВ

In recent years ecology has acquired special significance due to environmental deterio-ration and awareness of the need for caring attitude towards nature. Solution of environmental problems requires collaborative effort of specialists from different fields of expertise: ecology and natural resource management, economics, sociology, jurisprudence and terminology, since effective communication based on a common terminology base is key to successful cooperation. Some terms, however, have no exact analogues in other languages. Some terms lose their meaning in literal translation (“energy crops”, “invisible energy carriers”), while others (mostly one-word), consisting of several components, translate into a complete phrase (Naturerfahrungsraum - “space to gain experience with nature”). The article deals with German and international socio-ecological terms, which are difficult or impossible to literally translate into Russian while retaining the original meaning. The list also includes several terms that have literal translations (loan translations) into Russian, which do not explain the meanings of the terms to non-experts (“green bridge”, “ecological footprint”), as well as the terms located at the boundary of human ecology and related fields (economics, politics, urban ecology, etc.). The author argues the adviseability of using Sprachmittlung (mediation) instead of Ubersetzung (translation) for working with such terms and gives specific examples showing the metaphoricity of German socio-ecological vocabulary (“CNC land insurance”, “safari in a puddle”). Communication of meaning or language mediation (Sprachmittlung) is the subject of this study. The objects of the study are German as well as English (international) socio-ecological terms. Works by E.M. Kakzanova, I.G. Olshansky, Egon Becker and others lay the theoretical foundation of the research. Finally, the author draws conclusions about the peculiarities of communication of meaning of German and English socio-ecological terms.