Smoluchowski-Kramers approximation in the case of variable friction

We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the Smoluchowski-Kramers approximation. Some applications of the Smoluchowski-Kramers approximation to problems with fast oscillating or discontinuous coefficients are considered.Comment: already publishe

Wavelet analysis of beam-soil structure response for fast moving train

This paper presents a wavelet based approach for the vibratory analysis of beam-soil structure related to a point load moving along a beam resting on the surface. The model is represented by the Euler-Bernoulli equation for the beam, elastodynamic equation of motion for the soil and appropriate boundary conditions. Two cases are analysed: the model with a half space under the beam and the model where the supporting medium has a finite thickness. Analytical solutions for the displacements are obtained and discussed in relation to the used boundary conditions and the type of considered loads: harmonic and constant. The analysis in time-frequency and velocity-frequency domains is carried out for realistic systems of parameters describing physical properties of the model. The approximate displacement values are determined by applying a wavelet method for a derivation of the inverse Fourier transform. A special form of the coiflet filter used in numerical calculations allows to carry out analysis without loss of accuracy related to singularities appearing in wavelet approximation formulas, when dealing with standard filters and complex dynamic systems. © 2009 IOP Publishing Ltd

Using spatiotemporal modulation to draw tactile patterns in mid-air

No description supplie

The Effect of Soil Non-linearity on Mixed Traffic Railway Lines: Passenger vs Freight Loads

To add additional capacity to railway networks, freight services might be added to lines that have previously only be used for passenger services. Existing ballasted lines may have mixed subgrade conditions and thus the effect of increased axle loads on track behavior is unclear. Typically, such cases will result in elevated track deflections in comparison to passenger vehicles. As a result, the supporting subgrade experiences higher strain levels, which can fall into the large strain range. The related non-linear subgrade behavior plays an important role in track response but is challenging to model. As a solution, this paper presents a new semi-analytical numerical model, where the track is simulated analytically and allows for 1D wave propagation. The ground is modelled using a non-linear equivalent thin-layer finite element formulation. This allows for the subgrade stiffness to be updated in an iterative manner with minimal computational effort. A case study is presented to show that modest increases in axle load can have a marked effect on track deflections

Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m is an element of(0,1). Error estimates are obtained in the case m is an element of(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m is an element of(0,1/4) but play a crucial role in the formulation of the limit problem for m >= 1/4.Peer reviewe

Railway-induced ground vibrations – a review of vehicle effects

This paper is a review of the effect of vehicle characteristics on ground- and track borne-vibrations from railways. It combines traditional theory with modern thinking and uses a range of numerical analysis and experimental results to provide a broad analysis of the subject area. First, the effect of different train types on vibration propagation is investigated. Then, despite not being the focus of this work, numerical approaches to vibration propagation modelling within the track and soil are briefly touched upon. Next an in-depth discussion is presented related to the evolution of numerical models, with analysis of the suitability of various modelling approaches for analysing vehicle effects. The differences between quasi-static and dynamic characteristics are also discussed with insights into defects such as wheel/rail irregularities. Additionally, as an appendix, a modest database of train types are presented along with detailed information related to their physical attributes. It is hoped that this information may provide assistance to future researchers attempting to simulate railway vehicle vibrations. It is concluded that train type and the contact conditions at the wheel/rail interface can be influential in the generation of vibration. Therefore, where possible, when using numerical approach, the vehicle should be modelled in detail. Additionally, it was found that there are a wide variety of modelling approaches capable of simulating train types effects. If non-linear behaviour needs to be included in the model, then time domain simulations are preferable, however if the system can be assumed linear then frequency domain simulations are suitable due to their reduced computational demand

Alpha-invariants and purely log terminal blow-ups

We prove that the sum of the $\alpha$-invariants of two different Koll\'ar components of a Kawamata log terminal singularity is less than $1$.Comment: 12 page

Northern Eurasia Future Initiative (NEFI): facing the challenges and pathways of global change in the 21st century

During the past several decades, the Earth system has changed significantly, especially across Northern Eurasia. Changes in the socio-economic conditions of the larger countries in the region have also resulted in a variety of regional environmental changes that can have global consequences. The Northern Eurasia Future Initiative (NEFI) has been designed as an essential continuation of the Northern Eurasia Earth Science Partnership Initiative (NEESPI), which was launched in 2004. NEESPI sought to elucidate all aspects of ongoing environmental change, to inform societies and, thus, to better prepare societies for future developments. A key principle of NEFI is that these developments must now be secured through science-based strategies co-designed with regional decision makers to lead their societies to prosperity in the face of environmental and institutional challenges. NEESPI scientific research, data, and models have created a solid knowledge base to support the NEFI program. This paper presents the NEFI research vision consensus based on that knowledge. It provides the reader with samples of recent accomplishments in regional studies and formulates new NEFI science questions. To address these questions, nine research foci are identified and their selections are briefly justified. These foci include: warming of the Arctic; changing frequency, pattern, and intensity of extreme and inclement environmental conditions; retreat of the cryosphere; changes in terrestrial water cycles; changes in the biosphere; pressures on land-use; changes in infrastructure; societal actions in response to environmental change; and quantification of Northern Eurasia's role in the global Earth system. Powerful feedbacks between the Earth and human systems in Northern Eurasia (e.g., mega-fires, droughts, depletion of the cryosphere essential for water supply, retreat of sea ice) result from past and current human activities (e.g., large scale water withdrawals, land use and governance change) and potentially restrict or provide new opportunities for future human activities. Therefore, we propose that Integrated Assessment Models are needed as the final stage of global change assessment. The overarching goal of this NEFI modeling effort will enable evaluation of economic decisions in response to changing environmental conditions and justification of mitigation and adaptation efforts