Conditions for a Monotonic Channel Capacity

Motivated by results in optical communications, where the performance can degrade dramatically if the transmit power is sufficiently increased, the channel capacity is characterized for various kinds of memoryless vector channels. It is proved that for all static point-to-point channels, the channel capacity is a nondecreasing function of power. As a consequence, maximizing the mutual information over all input distributions with a certain power is for such channels equivalent to maximizing it over the larger set of input distributions with upperbounded power. For interference channels such as optical wavelength-division multiplexing systems, the primary channel capacity is always nondecreasing with power if all interferers transmit with identical distributions as the primary user. Also, if all input distributions in an interference channel are optimized jointly, then the achievable sum-rate capacity is again nondecreasing. The results generalizes to the channel capacity as a function of a wide class of costs, not only power.Comment: This is an updated and expanded version of arXiv:1108.039

Tools and analysis of spatio-temporal dynamics in heterogeneous aquifers: applications to artificial recharge and forced-gradient solute transport

This thesis deals with the development of tools and analysis to characterize and predict artificial recharge and radial convergent solute transport processes in heterogeneous media. The goal is to provide new insights to understand how heterogeneity, which is the main natural source of uncertainty in decision-making processes related with groundwater applications, can be controlled and its effects predicted for practical purposes in these topics. For hydrogeological applications, accurate modeling of phenomena is needed, but it is uncertain. Uncertainty is derived from the spatio-temporal random distribution of hydrodynamic (physical, chemical and biological) variables affecting groundwater processes, which is translated into random distribution of modeling parameters and equations. Such randomness is of two types: epistemic, when it can be reduced increasing the sample frequency of an experiment; aleatory, when it cannot be reduced when more information is analyzed. Sometimes hydrodynamic processes occur at so small scales that they become impossible to characterize with traditional methods, and from a practical perspective, this is analogous to deal with aleatoric model parameters. However, if some constitutive relationship (either empirically, theoretically or physically based) can be built between processes across different scales, then small-scale processes can be reproduced by equivalent large-scale model parameters. Uncertainty becomes amenable to be treated as epistemic randomness, and large-scale characterization techniques can be used to improve the description, interpretation or prediction of these processes. This thesis deals with these topics. The manuscript is composed by two main parts (the first on artificial recharge and the second on solute transport), each of them divided into three chapters. In chapter 1 of each part, a tool is developed to obtain quantitative information to model a selected variable at coarse grid resolutions. In the case of artificial recharge, satellite images are used to model the spatial variability of the infiltration capacity on top soils with a metric-scale detail. In the case of solute transport, a new method to estimate density from particle distribution is shown. In chapters 2, it is explored what processes occurring at the fine scales can affect the interpretation of artificial recharge and solute transport processes at larger scales. In the first part, a combined method that joins satellite images and field data along with a simple clogging model is used to display the equally-possible spatio-temporal mapping of the infiltration capacity of topsoil during artificial pond flooding activities. In the second part, numerical three-dimensional models are used to simulate transport in heterogeneous media under convergent radial flow to a well at fine scale. It is shown that an appropriate model framework can reproduce similar observations on contaminant temporal distribution at controlling section similar to those obtained in the field tracer tests. It is also provided a physical explanation to describe the so-called anomalous late-time behavior on breakthrough curves which is sometimes observed in the reality at larger scales. In the chapters 3, models are used to define the uncertainty around operating parameters in the optic of prediction and management on artificial recharge and solute transport. In the first case, a probability framework is built to define the engineering risk of management of artificial recharge ponds due to random variability of the initial distribution of infiltration, which controls several important clogging factors based on theoretical approaches. In the case of solute transport, it is discussed how equivalent parameters based on mass-transfer models can be related with the geometrical distribution of hydraulic parameters in anisotropic formation, when convergent flow tracer tests are used