Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure

5D BIM FOR CONSTRUCTION SITE SURVEYNG

The scope of work presented in this paper is to provide a BIM-based workflow supporting clients and contractors in construction site surveying. It is well known that BIM technology offers many profitable issues that benefit owners, designers and constructors, especially in terms of design efficiency and interoperability. Moreover, it can become a powerful instrument for the client’s team and the General Contractor all along the construction phase, starting from the construction site organization to answer the bid requests. It can also support the supervision of work progress and amount, and allow to periodically reconsider them in compliance with available resources. Starting from these statements, the authors have developed some studies to obtain a systematic and methodological approach for site surveying and optimization. Then, the research focuses primarily on the definition of proper requirements to outline a 5D site management throughout the whole construction process. After the definition of different needs for the different actors of construction process, the research moved to the possible BIM use for the satisfaction of these needs by the definition of customized parameters dealing with site spaces and facilities, quantities, time and cost management. The parameters have been identified to respond the needs of the on-field case study concerning the realization of a school complex in Cernusco sul Naviglio (Milan). Furthermore the field test proved efficiency and promptness to changes of the developed method in particular concerning scheduling optimization. By further inspections, this process is also supposed to become an instrument of dialog and comparison with the Health & Safety team, to verify work items clashes against health and safety on construction site

The Guard of Soils and of Their Rational Use in Lutsk District of the Volyn Region

Розглянуто раціональне використання земель при максимальному залученні їх до обігу за основним цільовим призначенням (використання під сільськогосподарські угіддя, лісові масиви, ставки, рекреацію та ін.), а також створення найкращих умов для високої продуктивності і найменших втрат праці й затрат із урахуванням їх екології та охорони.The rational use of soils according to their main setting (agricultural use, forest arrays, ponds, recreation) and creation of the most favourable terms for high productivity at the least losses of labour and money taking into account their ecology and guard are considered.Роботу виконано на кафедрі фізичної географії ВНУ ім. Лесі Українк

First passage times and distances along critical curves

We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate such curves with tunable fractal dimension $d_f$. We numerically compute the probability of first passage (in length or time) from one point on the edge of the semi-infinite plane to any point on the semi-circle of radius $R$. The scaled probability distributions have a variance which increases with $d_f$, a non-monotonic skewness, and tails that decay faster than a simple exponential. The latter is in sharp contrast to predictions based on fractional dynamics and provides an experimental signature for our model.Comment: 5 pages, 5 figure

Residence time and collision statistics for exponential flights: the rod problem revisited

Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.Comment: 9 pages, 8 figure

Chemical modification of wood induced by the traditional making procedures of bowed string musical instruments: the effect of alkaline treatments

Over the last few decades, chemical and physical studies on bowed string musical instruments have provided a better understanding of their wooden finished surface. Nevertheless, until now only a few of them investigated the effects of the chemical pre-treatments in the traditional making procedures. Those treatments are believed to affect wood properties, its interaction with the following treatments (i.e. varnish application) and its vibro-mechanical behaviour (that may contribute to the acoustical properties of musical instruments). In this study, two traditional alkaline treatments were applied to reference samples of spruce wood, the wood commonly used to make violins’ soundboards. An integrated analytical strategy, which combines infrared spectroscopy, analytical pyrolysis coupled to gas chromatography-mass spectrometry, and gel permeation chromatography, was employed to investigate the chemical alterations of lignocellulosic polymers (cellulose, hemicellulose, and lignin). Results have shown that the selected alkaline treatments induce the partial hydrolysis of the hemicellulose chains and a slight decrease in the crystallinity of cellulose. We could also prove: (i) the cleavage of lignin-carbohydrate complexes formed by the covalent bonds between hemicellulose and lignin in spruce wood, and (ii) the partial breaking of the hydrogen bonds network in cellulose. According to the literature, the alteration of the lignin-carbohydrate complexes is responsible for changes in wood mechanical behaviour. Hence, future perspectives of this research could outline new knowledge on the vibro-mechanical behaviour of the violin soundboard and the consequent acoustics

Manejo de buva em áreas cultivadas com milho safrinha e aveia.

A infestação de buva (Conyza spp) tem aumentado significativamente nas áreas de produção do sistema soja-trigo-milho especialmente nos estados do Paraná e Rio Grande do Sul. Foram conduzidos dois experimentos na safra 2009/2010 em uma propriedade rural do município de Campo Mourão, PR, com o objetivo de testar alternativas para o controle químico da buva, utilizando-se diferentes produtos e doses, aplicados na dessecação em pré-semeadura da soja, cultivada em áreas contíguas cobertas por palha de milho e de aveia. Foram aplicadas combinações de glifosato com diclosulan, flumioxazin, clorimuron-ethyl, imazetapyr, 2,4-0, paraquat+diuron e saflufenasil. É sabido que existe uma relação entre o tipo de cobertura e o tamanho das plantas de buva, o que pode influenciar no controle por ocasião da aplicação e que plantas menores são melhor controladas do que plantas mais desenvolvidas. Neste trabalho, 64% das plantas de buva na área com aveia estavam com. menos de 10 cm de altura e 36% entre 10 a 20 cm. Já na área com cobertura de milho safrinha apenas 20% das plantas estavam com menos de 10cm de altura, 56% entre 10 a 20 cm e outros 20% com mais de 20cm de altura. Embora não seja possível comparar os dois experimentos entre si, ficou evidente o melhor controle obtido pela maioria dos tratamentos quando aplicados sobre a cobertura de aveia, o que pode ser explicado pela diferença de tamanho das plantas por ocasião das aplicações. A combinação de glifosato com 2,4-0 ou herbicidas que possuem ação residual, complementada com aplicação sequencial que envolve um produto de contato tem mostrado ser uma importante forma de manejo químico para o controle da buva

Interferência da buva em áreas cultivadas com soja.

O aumento de incidência de buva nas áreas de cultivo da soja era previsto como consequência da adoção do plantio direto e das características inerentes a essa planta daninha, como o tamanho de suas sementes, a prolificidade, a dispersão pelo vento e a germinação na superfície do solo. A buva é uma planta nativa das Américas e sempre esteve presente na relação das principais espécies invasoras no Brasil. Nos últimos anos esta espécie passou a ser uma das principais infestantes das áreas de cultivo do sistema soja-milho-trigo na região sul do Brasil. O objetivo do trabalho foi analisar a interferência causada pelas plantas de buva na cultura da soja. Três experimentos foram conduzidos na safra 2008/2009 e um na safra 2009/2010, todos em áreas comercias escolhidas aleatoriamente e cujo manejo da área e do cultivo havia sido feito pelo produtor. A metodologia constou da determinação do rendimento de grãos em relação a diferentes níveis de infestação da buva. Paralelamente, foram coletadas amostras de soja provenientes do graneleiro de uma colheitadeira que operava na área, para a classificação dos grãos quanto ao teor de umidade e impureza. Os resultados indicam que a interferência da buva cultura da soja não se limita a reduções do rendimento de grãos, cujos valores em média apresentaram perdas que variaram de 1174Kg ha-' a 1469 Kg há-' nos maiores níveis de infestação, o que correspondeu a até 48% de perdas em relação a área sem infestação. Nos níveis mais baixos de infestação as perdas relativas de rendimento em comparação com as áreas sempre limpas variaram no diferentes experimentos de 2% a quase 5%. A presença da buva. interferiu também na classificação comercial da soja, chegando a aumentar a umidade dos grão em percentuais que variaram de 2 a 7% e a impureza de 1,8% a mais de 6% dependendo do nível de infestação