On the equivalence of modes of convergence for log-concave measures

An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note, we explore the extent to which different notions of distance between probability measures are comparable for log-concave distributions. Our results imply that weak convergence of isotropic log-concave distributions is equivalent to convergence in total variation, and is further equivalent to convergence in relative entropy when the limit measure is Gaussian.Comment: v3: Minor tweak in exposition. To appear in GAFA seminar note

Remarks on the KLS conjecture and Hardy-type inequalities

We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann Poincar\'e constant on $\Omega$ to that of the cone and Lebesgue measures on $\partial \Omega$; these may be bounded via the curvature of $\partial \Omega$. A second reduction is obtained to the class of harmonic functions on $\Omega$. We also study the relation between the Poincar\'e constant of a log-concave measure $\mu$ and its associated K. Ball body $K_\mu$. In particular, we obtain a simple proof of a conjecture of Kannan--Lov\'asz--Simonovits for unit-balls of $\ell^n_p$, originally due to Sodin and Lata{\l}a--Wojtaszczyk.Comment: 18 pages. Numbering of propositions, theorems, etc.. as appeared in final form in GAFA seminar note

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Parameter distributions for the drag-based modeling of CME propagation

In recent years, ensemble modeling has been widely employed in space weather to estimate uncertainties in forecasts. We here focus on the ensemble modeling of Coronal Mass Ejections (CME) arrival times and arrival velocities using a drag-based model, which is well-suited for this purpose due to its simplicity and low computational cost. Although ensemble techniques have previously been applied to the drag-based model, it is still not clear how to best determine distributions for its input parameters, namely the drag parameter and the solar wind speed. The aim of this work is to evaluate statistical distributions for these model parameters starting from a list of past CME-ICME events. We employ LASCO coronagraph observations to measure initial CME position and speed, and in situ data to associate them with an arrival date and arrival speed. For each event we ran a statistical procedure to invert the model equations, producing parameters distributions as output. Our results indicate that the distributions employed in previous works were appropriately selected, even though they were based on restricted samples and heuristic considerations. On the other hand, possible refinements to the current method are also identified, such as the dependence of the drag parameter distribution on the CME being accelerated or decelerated by the solar wind, which deserve further investigation

Prediction of Solar Proton Event Fluence spectra from their Peak flux spectra

Solar Proton Events (SPEs) are of great importance and significance for the study of Space Weather and Heliophysics. These populations of protons are accelerated at high energies ranging from a few MeVs to hundreds of MeVs and can pose a significant hazard both to equipment on board spacecrafts as well as astronauts as they are ionizing radiation. The ongoing study of SPEs can help to understand their characteristics, relative underlying physical mechanisms, and help in the design of forecasting and nowcasting systems which provide warnings and predictions. In this work, we present a study on the relationships between the Peak Flux and Fluence spectra of SPEs. This study builds upon existing work and provides further insights into the characteristics and the relationships of SPE Peak flux and Fluence spectra. Moreover it is shown how these relationships can be quantified in a sound manner and exploited in a simple methodology with which the Fluence spectrum of an SPE can be well predicted from its given Peak spectrum across two orders of magnitude of proton energies, from 5 MeV to 200 MeV. Finally it is discussed how the methodology in this work can be easily applied to forecasting and nowcasting systems

Multiscale friction in lubricant-surface systems for high performance transmissions under mild wear

The lubricant-surface system is complex in nature and can significantly affect the frictional performance of high-performance transmission systems. The complexity stems from the coupled mechanical and chemical phenomena that occur at the interfacial tooth conjunctions. A combined analytical and precision experimental approach is presented to analyse the salient parameters of the lubricant-surface system. A multiscale procedure comprising topographical measurement, pin-on-disc tribometry, atomic force microscopy in lateral force mode, X-ray photo-electron spectroscopy and continuum contact mechanics analysis under mixed non-Newtonian thermo-elastohydrodynamics is used to describe the formation of a tribo-film, as well as wear and frictional characteristics of the lubricant-surface system. The contribution of chemisorbed and physisorbed bonded tribo-film on the boundary coefficient of friction is ascertained at different physical scales. Therefore, the paper presents a novel multiscale analysis, promoting improved understanding of the complex interactions between mechanisms of friction, wear and surface chemistry

Heat generation and transfer in automotive dry clutch engagement

Dynamic behaviour of automotive dry clutches depends on the frictional characteristics of the contact between the friction lining material, the flywheel, and the pressure plate during the clutch engagement process. During engagement due to high interfacial slip and relatively high contact pressures, generated friction gives rise to contact heat, which affects the material behaviour and the associated frictional characteristics. In practice excess interfacial slipping and generated heat during torque transmission can result in wear of the lining, thermal distortion of the friction disc, and reduced useful life of the clutch. This paper provides measurement of friction lining characteristics for dry clutches for new and worn state under representative operating conditions pertaining to interfacial slipping during clutch engagement, applied contact pressures, and generated temperatures. An analytical thermal partitioning network model of the clutch assembly, incorporating the flywheel, friction lining, and the pressure plate is presented, based upon the principle of conservation of energy. The results of the analysis show a higher coefficient of friction for the new lining material which reduces the extent of interfacial slipping during clutch engagement, thus reducing the frictional power loss and generated interfacial heating. The generated heat is removed less efficiently from worn lining. This might be affected by different factors observed such as the reduced lining thickness and the reduction of density of the material but mainly because of poorer thermal conductivity due to the depletion of copper particles in its microstructure as the result of wear. The study integrates frictional characteristics, microstructural composition, mechanisms of heat generation, effect of lining wear, and heat transfer in a fundamental manner, an approach not hitherto reported in literature

An analytical approach for prediction of elastohydrodynamic friction with inlet shear heating and starvation

An analytical friction model is presented, predicting the coefficient of friction in elastohydrodynamic (EHD) contacts. Three fully formulated SAE 75W-90 axle lubricants are examined. The effect of inlet shear heating (ISH) and starvation is accounted for in the developed friction model. The film thickness and the predicted friction are compared with experimental measurements obtained through optical interferometry and use of a mini traction machine. The results indicate the significant contribution of ISH and starvation on both the film thickness and coefficient of friction. A strong interaction between those two phenomena is also demonstrated, along with their individual and combined contribution on the EHD friction