Richardson Model Research Articles

Geometrical Properties of Turbulent Dispersion

It is shown that the shape statistics of four correlated particles, known as a tetrad, in a direct numerical simulation of three-dimensional homogeneous isotropic turbulence agree very well with a simple diffusion equation with a separation-dependent eddy diffusivity. The latter is essentially an extension of Richardson's model for particle-pair dispersion to tetrads. It is also shown that the degree of elongation of the tetrad in the inertial subrange of a turbulentlike flow is controlled by the exponent, m, in an eddy diffusivity of the form K(r)[proportionality]r(m) where r is the interparticle separation, becoming more elongated as m increases in the range 0≤m<2.

Fractal analysis of dendrites morphology using modified Richardson's and box counting method.

Fractal analysis has proven to be a useful tool in analysis of various phenomena in numerous naturel sciences including biology and medicine. It has been widely used in quantitative morphologic studies mainly in calculating the fractal dimension of objects. The fractal dimension describes an object's complexity: it is higher if the object is more complex, that is, its border more rugged, its linear structure more winding, or its space more filled. We use a manual version of Richardson's (ruler-based) method and a most popular computer-based box-counting method applying to the problem of measuring the fractal dimension of dendritic arborization in neurons. We also compare how these methods work with skeletonized vs. unskeletonized binary images. We show that for dendrite arborization, the mean box dimension of unskeletonized images is significantly larger than that of skeletonized images. We also show that the box-counting method is sensitive to an object's orientation, whereas the ruler-based dimension is unaffected by skeletonizing and orientation. We show that the mean fractal dimension measured using the ruler-based method is significantly smaller than that measured using the box-counting method. Whereas the box-counting method requires defined usage that limits its utility for analyzing dendritic arborization, the ruler-based method based on Richardson's model presented here can be used more liberally. Although this method is rather tedious to use manually, an accessible computer-based implementation for the neuroscientist has not yet been made available.

Description of two-particle transfer in superfluid systems

Exact results of pair transfer probabilities for the Richardson model with equidistant or random level spacing are presented. The results are then compared either to particle-particle random-phase approximation (ppRPA) in the normal phase or quasiparticle random-phase approximation (QRPA) in the superfluid phase. We show that both ppRPA and QRPA are globally well reproducing the exact case although some differences are seen in the superfluid case. In particular, the QRPA overestimates the pair transfer probabilities to excited states in the vicinity of the normal-superfluid phase transition, which might explain the difficulty in detecting collective pairing phenomena as, for example, the giant pairing vibration. The shortcoming of QRPA can be traced back to the breaking of particle number that is used to incorporate pairing. A method based on direct diagonalization of the Hamiltonian in the space of two quasiparticles projected onto good particle number is shown to improve the description of pair transfer probabilities in superfluid systems.

The Heine–Stieltjes correspondence and the polynomial approach to the Gaudin–Richardson models

The Heine–Stieltjes correspondence is extended and applied to solve Bethe ansatz equations of the Gaudin–Richardson models, from which the extended Heine–Stieltjes polynomial approach to these models is proposed. As examples for the application of this approach, exact solutions of the standard two-site Bose–Hubbard model and the standard pairing model for nuclei are formulated from the corresponding polynomials.

Practical Reasoning, Impartiality and the European Patent Office: The Legal Regulation of Biotechnology

Abstract:The article argues in favour of a different conceptualisation of the role of the European Patent Office, and of the mode of reasoning that the EPO ought to deploy, so as to decide cases concerning the patentability of gene related inventions such as diagnostic tests, and questions regarding the regulation of therapeutic cloning. Richardson's model of specifying norms offers an important alternative to the models based on cost‐benefit analysis and neutral application of the appropriate norm by administrative agencies. Specificationism stresses the importance of revising the ends of policy, coming up with a new norm, the product of creative synthesis of the content of conflicting norms. The article adds to this model the idea that the revision of ends requires a strong deliberative democracy, based on the notion of the practically wise regulator, who can apply principles correctly, as these cannot be usefully applied in difficult situations by people who lack experience, insight, and character. Given the current discussion to establish a unitary EU patent, the thesis advanced here is that the patent system in Europe ought to endorse elements of deliberative democracy, enhancing the importance of civil society in the European decision making processes.

Bethe ansatz and ordinary differential equation correspondence for degenerate Gaudin models

In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only reduce the number of relevant states in the Hilbert space by a non negligible fraction, they also allow to write the relevant equations in the form of sparse matrix equations. Moreover, we introduce a new inversion method based on a basis of barycentric polynomials which leads to a more stable and efficient root extraction which most importantly avoids the necessity of working with arbitrary precision. As an example we show the results of our procedure applied to the Richardson model on a square lattice.

Large scale evaluation of single storm and short/long term erosivity index models

Rainfall erosivity of the Revised Universal Soil Loss Equation (RUSLE) is influenced by the type, amount, and intensity of storm. In this research, rainfall data from 18 recording rain gauge stations were collected and analyzed. Further, their single storm, daily, monthly, and annual erosion indices were calculated and estimated by different models. Duration of each rainfall was divided into 15 min intervals. Intensity and energy of each interval, maximum rainfall intensity of 30 min, total energy of each rainfall, and erosivity index of every single storm were calculated. Furthermore, Cooley's model for single storm was evaluated and its coefficients were estimated. For daily rainfall erosion index prediction, Richardson's model was assessed and its coefficients were also estimated. A new power model based on monthly rainfall was proposed in order to predict monthly rainfall erosion index. For the estimation of the annual rainfall erosion index, the Arnoldus model was evaluated and its coefficients were estimated. The coefficients for all equations were also determined using multiple regression. According to the calibrated Arnoldus model, an iso-rainfall erosion index map was drawn for the studied area consisting of 150 rain gauge information. The results indicated that models of Cooley, Richardson, Arnoldus, and the newly proposed model for monthly rainfall erosion index provide a reasonable agreement with the rainfall characteristics of the studied area.

Structure of typical states of a disordered Richardson model and many-body localization

We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We study the onset of delocalization in typical states (many-body delocalization) and the delocalized phase which extends over the whole range of coupling strength in the thermodynamic limit. We find a relation between the inverse participation ratio, the Edwards-Anderson order parameter and the average Hamming distance between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit. We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses.

The two-type continuum Richardson model: nondependence of the survival of both types on the initial configuration

We consider the model of Deijfen, Häggström and Bagley (2004) for competing growth of two infection types in R d , based on the Richardson model on Z d . Stochastic ball-shaped infection outbursts transmit the infection type of the center to all points of the ball that are not yet infected. Relevant parameters of the model are the initial infection configuration, the (type-dependent) growth rates, and the radius distribution of the infection outbursts. The main question is that of coexistence: Which values of the parameters allow the unbounded growth of both types with positive probability? Deijfen, Häggström and Bagley (2004) conjectured that the initial configuration is basically irrelevant for this question, and gave a proof for this under strong assumptions on the radius distribution, which, e.g. do not include the case of a deterministic radius. Here we give a proof that does not rely on these assumptions. One of the tools to be used is a slight generalization of the model with immune regions and delayed initial infection configurations.

The two-type continuum Richardson model: nondependence of the survival of both types on the initial configuration

We consider the model of Deijfen, Häggström and Bagley (2004) for competing growth of two infection types in Rd, based on the Richardson model on Zd. Stochastic ball-shaped infection outbursts transmit the infection type of the center to all points of the ball that are not yet infected. Relevant parameters of the model are the initial infection configuration, the (type-dependent) growth rates, and the radius distribution of the infection outbursts. The main question is that of coexistence: Which values of the parameters allow the unbounded growth of both types with positive probability? Deijfen, Häggström and Bagley (2004) conjectured that the initial configuration is basically irrelevant for this question, and gave a proof for this under strong assumptions on the radius distribution, which, e.g. do not include the case of a deterministic radius. Here we give a proof that does not rely on these assumptions. One of the tools to be used is a slight generalization of the model with immune regions and delayed initial infection configurations.

ISOVECTOR PAIRING EFFECT ON NUCLEAR MOMENT OF INERTIA AT FINITE TEMPERATURE IN N = Z EVEN–EVEN SYSTEMS

Expressions of temperature-dependent perpendicular (ℑ⊥) and parallel (ℑ‖) moments of inertia, including isovector pairing effects, have been established using the cranking method. They are derived from recently proposed temperature-dependent gap equations. The obtained expressions generalize the conventional finite-temperature BCS (FTBCS) ones. Numerical calculations have been carried out within the framework of the schematic Richardson model as well as for nuclei such as N = Z, using the single-particle energies and eigenstates of a deformed Woods–Saxon mean-field. ℑ⊥ and ℑ‖ have been studied as a function of the temperature. It has been shown that the isovector pairing effect on both the perpendicular and parallel moments of inertia is non-negligible at finite temperature. These correlations must thus be taking into account in studies of warm rotating nuclei in the N ≃ Z region.

The role of trading intensity estimating the implicit bid–ask spread and determining transitory effects

In this paper, we investigate the information content of trading intensity applying the Madhavan, Richardson and Roomans (1997) structural model to express trading intensity as trading momentum in duration and volume. Using both transactions and intraday data from the Helsinki Stock Exchange Limit Order Bookmarket, we find that momentum in duration and volume enhances the information effect. We reach this conclusion based on the parametric effect determined by the sign and the magnitude of the coefficients associated with the trading intensity variables, the trading effect determined by the ratio of transitory effects to permanent effects, and the economic effect determined by the size of the implicit bid–ask spread. While we find that the implicit bid–ask spread and transitory effects are decreasing toward the end of the trading day in consistency with information models in the literature, there is a surge of trades at the market close, most probably due to information uncertainty at market opening in New York.

The dynamics of asymmetric interactions: Some insights from formal theory and Richardson models

Sometimes a large power attempts to influence the actions of one or more smaller agents that may be influenced by other small agents. This situation gives rise to amixed system of symmetric and asymmetric interactions and each case of this kind seems to have unique characteristics. This article asks, can a formal approach bring out some general features of such interactions? We extend a well-known model of the dynamics of arms races in new directions, and produce some counterintuitive results that may have interest for policy debates.

Nonperturbative quantum dynamics of the order parameter in the BCS pairing model

We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different Hilbert spaces of single-particle and paired/empty states. This allows us to factorize the full thermodynamic partition function into a combination of simple terms associated with real spins on singly-occupied states and the partition function of the quantum XY-model for Anderson pseudospins associated with the paired/empty states. Using coherent-state path-integral, we calculate the effects of superconducting phase fluctuations exactly. The contribution of superconducting amplitude fluctuations to the partition function in the broken-symmetry phase is shown to follow from the Bogoliubov-de Gennes equations in imaginary time. These equations in turn allow several interesting mappings, e.g., they are shown to be in a one-to-one correspondence with the one-dimensional Schr\"odinger equation in supersymmetric Quantum Mechanics. However, the most practically useful approach to calculate functional determinants is found to be via an analytical continuation of the quantum order parameter to real time, \Delta(\tau -> it), such that the problem maps onto that of a driven two-level system. The contribution of a particular dynamic order parameter to the partition function is shown to correspond to the sum of the Berry phase and dynamic phase accumulated by the pseudospin. We also examine a family of exact solutions for two-level-system dynamics on a class of elliptic functions and suggest a compact expression to estimate the functional determinants on such trajectories. The possibility of having quantum soliton solutions co-existing with classical BCS mean-field is discussed.

SOLAR RADIATION ESTIMATION FROM RAINFALL AND TEMPERATURE DATA IN ARID AND SEMI-ARID CLIMATES OF IRAN

Precipitation and air temperature data, only, are often recorded at meteorological stations, with radiation beingmeasured at very few weather stations, especially in developing countries. Therefore there arises a need for suitablemodels to estimate solar radiation for a completion of data sets. This paper is about an evaluation of eight models foran estimation of daily solar radiation (Q) from commonly measured variables in six synoptic stations of Iran, namely:Mashhad, Kerman, Tabriz, Esfehan, Hamedan and Zanjan using daily rainfall and temperature data for a duration ofthree years of 2000, 2001 and 2002. These stations represent several arid and semiarid sub-climates of Iran as basedon extended-De Martonne climatic classification (semiarid-cold: Mashhad and Tabriz, arid-cold: Esfehan, Kerman,semiarid-extracold: Hamedan and Zanjan). The STATISTICA (ver. 6.0) software was employed for non-linearmultivariate regression. The results indicated that most of the models overestimated in lower values of solar radiationwhile underestimating in the higher ranges, indicating a systematic error. Performance of the models was evaluatedbased on the Root Mean Square Errors (RMSE) as well as R2. RMSE ranged from 1.14 to 7.76 Cal cm-2min-1 for thewhole data range and in all the six stations. Among the eight models, the Richardson model rendered the bestagreement with the measured data in Kerman and Zanjan stations. In case of Hamedan station, Bristow and Campbellmodel was the most suitable. As for Tabriz station, De Jong and Stewart model using rainfall and range of dailytemperature data led to the best performance. In Mashhad station, McCaskill equation can be recommended. Analysisof the data in Esfehan station showed no significant difference among the models. Due to variation in equations'performances, to come to valid conclusions and to choose the most suitable radiation models, further study would berequired from other climatic regions the country.

Isovector neutron-proton pairing with particle number projected BCS

The particle number projected BCS (PBCS) approximation is tested against the exact solution of the SO(5) Richardson-Gaudin model for isovector pairing in a system of nondegenerate single-particle orbits. Two isovector PBCS wave functions are considered. One is constructed as a single proton-neutron pair condensate; the other corresponds to a product of a neutron pair condensate and a proton pair condensate. The PBCS equations are solved using a recurrence method and the analysis is performed for systems with an equal number of neutrons and protons distributed in a sequence of equally spaced fourfold (spin-isospin) degenerate levels. The results show that although PBCS offers significant improvement over BCS, the agreement of PBCS with the exact solution is less satisfactory than in the case of the SU(2) Richardson model for pairing between like particles.

Bethe ansatz approach to quench dynamics in the Richardson model

By instantaneously changing a global parameter in an extended quantum system, an initially equilibrated state will afterwards undergo a complex nonequilibrium unitary evolution whose description is extremely challenging. A nonperturbative method giving a controlled error in the long time limit remained highly desirable to understand general features of the quench induced quantum dynamics. In this paper we show how integrability (via the algebraic Bethe ansatz) gives one numerical access, in a nearly exact manner, to the dynamics resulting from a global interaction quench of an ensemble of fermions with pairing interactions (Richardson’s model). This possibility is deeply linked to the specific structure of this particular integrable model which gives simple expressions for the scalar product of eigenstates of two different Hamiltonians. We show how, despite the fact that a sudden quench can create excitations at any frequency, a drastic truncation of the Hilbert space can be carried out therefore allowing access to large systems. The small truncation error which results does not change with time and consequently the method grants access to a controlled description of the long time behavior which is a hard to reach limit with other numerical approaches.

Particle-number conservation in thermodynamic systems within the Richardson model

To describe thermal pairing systems, an approach that combines the modified BCS method and the Lipkin-Nogami particle-number projection method is proposed. The expressions of the thermal pairing gap and internal energy are derived. The latter are numerically studied as a function of the temperature within the Richardson model.

The calcium silicate hydrates

This article is concerned with the calcium silicate hydrates, including crystalline minerals and the extremely variable and poorly ordered phase (C-S-H) that is the main binding phase in most concrete. Up-to-date composition and crystal-structure information is tabulated for the most important crystalline calcium (alumino) silicate hydrates and related phases. A number of models for the nanostructure of C-S-H are summarized and compared and it is shown that there is much more of a consensus than might seem apparent at first sight. The value of the recently solved structures of 1.4 nm tobermorite and jennite, together with those of jaffeite and metajennite, for visualizing the nanostructural elements present in the models is demonstrated. The importance of Hal Taylor's contribution to the solution of the structure of jennite is highlighted. The applicability of Richardson and Groves' model is demonstrated using experimental composition-structure observations on the nature of C-S-H in a Portland cement-fly ash blend.

The revised learning process questionnaire: A validation of a Western model of students' study approaches to the South Pacific context using confirmatory factor analysis

Research evidence seems to suggest that the social and cultural environments influence students' approaches to their study. This social and cultural contention has led to the rethinking and reconceptualization of theories (e.g. Biggs, 1987; Marton & Säljö, 1976) pertaining to student approaches to learning (SAL) in academic settings. The present research discusses two separate empirical studies on student learning approaches situated in the South Pacific region with two respective cohorts of secondary students. Study I involved the examination of secondary Pacific Islands students in their learning approaches using a modified version of Biggs' (1987) original Learning Process Questionnaire (LPQ). Study II involved the administration of a revised version of the LPQ (R-LPQ-2F; Kember, Biggs, & Leung, 2004) to another cohort of secondary Pacific Islands students. The first sample included 2,150 (1,285 girls, 865 boys) students and the second sample included 2,295 (1,363 girls, 932 boys) students. The factor structures of approaches to learning were examined by means of confirmatory factor analysis (CFA) using the LISREL program. Different a priori models were hypothesized and tested. Results of Study I indicated a two-factor structure solution to Biggs' LPQ, supporting Richardson's (1994) theoretical model of learning and emphasized the factors of Reproducing and Meaning. Study II indicated a hierarchical organization of two main study approaches - deep and surface - that are structured as higher-order factors and a defined by four first-order factors. The results from the two studies accentuate the important argument for the rethinking and reconceptualization of learning approaches, as well as for the redevelopment and modification of learning inventories such as the LPQ. They also suggest the importance of situating the theoretical paradigm of learning approaches in a social and cultural environment.