Functional Methods and Effective Potentials for Nonlinear Composites

A formulation of variational principles in terms of functional integrals is proposed for any type of local plastic potentials. The minimization problem is reduced to the computation of a path integral. This integral can be used as a starting point for different approximations. As a first application, it is shown how to compute to second-order the weak-disorder perturbative expansion of the effective potentials in random composite. The three-dimensional results of Suquet and Ponte-Casta\~neda (1993) for the plastic dissipation potential with uniform applied tractions are retrieved and extended to any space dimension, taking correlations into account. In addition, the viscoplastic potential is also computed for uniform strain rates.Comment: 20 pages, accepted for publication in JMP

Modeling Fertilizer Demand in Cotton-Producing Villages of Benin: Does Price Matter in a Centralized Distribution System?

Cotton is a strategic crop in Benin's economy and fertilizer is a crucial necessity for its development. Fertilizer supply is awkwardly cotton-oriented and depends totally on imports. Spurious liberalization, characterized by partial state withdrawal combined with a rigid distribution agreement between the state, fertilizer traders and farmers’ cooperatives, led to a drastic decline in fertilizer use and cotton production. Although fertilizer consumption resumed timidly with reforms, the supply system remained centralized (importers’ licensing, distribution quotas, price administration). This study inquired whether price is relevant in fertilizer demand in such a business environment. Randomly-selected 577 cotton farmers from purposively-chosen 191 cotton-producing villages, were interviewed about fertilizer use and distribution using structured questionnaires. Determinants of average villagelevel fertilizer demand, elicited using a multiple regression model with a joint agronomic and marketing perspective, included at 5% or 1% significance level: the region’s dummy, share of cotton in cultivated area, rural roads’ density, distance ‘village store - farmer’s fields, and off-farm income. Other non-negligible factors included: estimated cost price, soil degradation rate, diffusion rate of water and soil conservation techniques, proportion of leased land area and distance ‘farmer’s house - local agricultural market’. Despite an administered pan-territorial district-level price, fertilizer demand was still sensitive to the actual farm-gate prices. However, the business environment had a stronger influence. The policy levers to increase fertilizer use intensity include the development of road and market infrastructures, promotion of market orientation of farming and off-farm activities, wise liberalization of fertilizer retail market, and reform of the licensing system

Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3

We have analyzed the morphology of ferroelectric domains in very thin films of multiferroic BiFeO3. Unlike the more common stripe domains observed in thicker films BiFeO3 or in other ferroics, the domains tend not to be straight, but irregular in shape, with significant domain wall roughening leading to a fractal dimensionality. Also contrary to what is usually observed in other ferroics, the domain size appears not to scale as the square root of the film thickness. A model is proposed in which the observed domain size as a function of film thickness can be directly linked to the fractal dimension of the domains.Comment: 4 pages, 3 figure

Integrating aerodynamics and structures in the minimum weight design of a supersonic transport wing

An approach is presented for determining the minimum weight design of aircraft wing models which takes into consideration aerodynamics-structure coupling when calculating both zeroth order information needed for analysis and first order information needed for optimization. When performing sensitivity analysis, coupling is accounted for by using a generalized sensitivity formulation. The results presented show that the aeroelastic effects are calculated properly and noticeably reduce constraint approximation errors. However, for the particular example selected, the error introduced by ignoring aeroelastic effects are not sufficient to significantly affect the convergence of the optimization process. Trade studies are reported that consider different structural materials, internal spar layouts, and panel buckling lengths. For the formulation, model and materials used in this study, an advanced aluminum material produced the lightest design while satisfying the problem constraints. Also, shorter panel buckling lengths resulted in lower weights by permitting smaller panel thicknesses and generally, by unloading the wing skins and loading the spar caps. Finally, straight spars required slightly lower wing weights than angled spars

Application of multidisciplinary optimization methods to the design of a supersonic transport

An optimization design method is discussed. This method is based on integrating existing disciplinary analysis and sensitivity analysis techniques by means of generalized sensitivity equations. A generic design system implementing this method is described. The system is being used to design the configuration and internal structure of a supersonic transport wing for optimum performance. This problem combines the disciplines of linear aerodynamics, structures, and performance. Initial results which include the disciplines of aerodynamics and structures in a conventional minimum weight design under static aeroelastic constraints are presented

Comparing and modeling land use organization in cities

The advent of geolocated ICT technologies opens the possibility of exploring how people use space in cities, bringing an important new tool for urban scientists and planners, especially for regions where data is scarce or not available. Here we apply a functional network approach to determine land use patterns from mobile phone records. The versatility of the method allows us to run a systematic comparison between Spanish cities of various sizes. The method detects four major land use types that correspond to different temporal patterns. The proportion of these types, their spatial organization and scaling show a strong similarity between all cities that breaks down at a very local scale, where land use mixing is specific to each urban area. Finally, we introduce a model inspired by Schelling's segregation, able to explain and reproduce these results with simple interaction rules between different land uses.Comment: 9 pages, 6 figures + Supplementary informatio

Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams

We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.Comment: 6 pages, 6 figures, Lette

Surface effects on nanowire transport: numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation-times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer. In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with existing theory. However, the effect is seen to be quite small (a few per cent) for realistic values of the wire parameters even at the highest practical magnetic fields. Physical insights emerging from the results are discussed.Comment: 15 pages, 7 figure