Mathematical Formalism for Isothermal Linear Irreversibility

We prove the equivalence among symmetricity, time reversibility, and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of the coefficients of the equations is given. The existence of a linear stationary irreversible process is established. Concerning reversibility, we show that there is a contradistinction between any 1-dimensional stationary Gaussian process and stationary Gaussian process of dimension $n>1$. A concrete criterion for differentiating stationarity and sweeping behavior is also obtained. The mathematical result is a natural generalization of Einstein's fluctuation-dissipation relation, and provides a rigorous basis for the isothermal irreversibility in a linear regime which is the basis for applying Onsager's theory to macromolecules in aqueous solution.Comment: 15 page

BRST invariance and de Rham-type cohomology of 't Hooft-Polyakov monopole

We exploit the 't Hooft-Polyakov monopole to define closed algebra of the quantum field operators and the BRST charge $Q_{BRST}$. In the first-class configuration of the Dirac quantization, by including the $Q_{BRST}$-exact gauge fixing term and the Faddeev-Popov ghost term, we find the BRST invariant Hamiltonian to investigate the de Rham-type cohomology group structure for the monopole system. The Bogomol'nyi bound is also discussed in terms of the first-class topological charge defined on the extended internal 2-sphere.Comment: 8 page

Nexus of thermal resilience and energy efficiency in buildings: A case study of a nursing home

Extreme weather events become more frequent and severe due to climate change. Although energy efficiency technologies can influence thermal resilience of buildings, they are traditionally studied separately, and their interconnections are rarely quantified. This study developed a methodology of modeling and analysis to provide insights into the nexus of thermal resilience and energy efficiency of buildings. We conducted a case study of a real nursing home in Florida, where 12 patients died during Hurricane Irma in 2017 due to HVAC system power loss, to understand and quantify how passive and active energy efficiency measures (EEMs) can improve thermal resilience to reduce heat-exposure risk of patients. Results show that passive measures of opening windows and doors for natural ventilation, as well as miscellaneous load reduction, are very effective in eliminating the extreme dangerous occasions. However, to maintain safe conditions, active measures such as on-site power generators and thermal storage are also needed. The nursing home was further studied by changing its location to two other cities: San Francisco (mild climate) and Chicago (cold winter and hot summer). Results revealed that the EEMs' impacts on thermal resilience vary significantly by climate and building characteristics. The study also estimated the costs of EEMs to help stakeholders prioritize the measures. Passive measures that may not save energy may greatly improve thermal resilience, and thus should be considered in building design or retrofit. Findings from this study indicate energy efficiency technologies should be evaluated not only by their energy savings performance but also by their influence on a building's resilience to extreme weather events

A version of the Glimm method based on generalized Riemann problems

We introduce a generalization of Glimm's random choice method, which provides us with an approximation of entropy solutions to quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend on the unknown as well as on the time and space variables. The method is based on local approximate solutions of the generalized Riemann problem, which form building blocks in our scheme and allow us to take into account naturally the effects of the flux and source terms. To establish the nonlinear stability of these approximations, we investigate nonlinear interactions between generalized wave patterns. This analysis leads us to a global existence result for quasilinear hyperbolic systems with source-term, and applies, for instance, to the compressible Euler equations in general geometries and to hyperbolic systems posed on a Lorentzian manifold.Comment: 34 page