Hard squares with negative activity

We show that the hard-square lattice gas with activity z= -1 has a number of remarkable properties. We conjecture that all the eigenvalues of the transfer matrix are roots of unity. They fall into groups (``strings'') evenly spaced around the unit circle, which have interesting number-theoretic properties. For example, the partition function on an M by N lattice with periodic boundary condition is identically 1 when M and N are coprime. We provide evidence for these conjectures from analytical and numerical arguments.Comment: 8 page

Integrated Heat Pump HVAC Systems for Near-Zero-Energy Homes - Business Case Assessment

The long range strategic goal of the Department of Energy's Building Technologies (DOE/BT) Program is to create, by 2020, technologies and design approaches that enable the construction of net-zero energy homes at low incremental cost (DOE/BT 2005). A net zero energy home (NZEH) is a residential building with greatly reduced needs for energy through efficiency gains, with the balance of energy needs supplied by renewable technologies. While initially focused on new construction, these technologies and design approaches are intended to have application to buildings constructed before 2020 as well resulting in substantial reduction in energy use for all building types and ages. DOE/BT's Emerging Technologies (ET) team is working to support this strategic goal by identifying and developing advanced heating, ventilating, air-conditioning, and water heating (HVAC/WH) technology options applicable to NZEHs. Although the energy efficiency of heating, ventilating, and air-conditioning (HVAC) equipment has increased substantially in recent years, new approaches are needed to continue this trend. Dramatic efficiency improvements are necessary to enable progress toward the NZEH goals, and will require a radical rethinking of opportunities to improve system performance. The large reductions in HVAC energy consumption necessary to support the NZEH goals require a systems-oriented analysis approach that characterizes each element of energy consumption, identifies alternatives, and determines the most cost-effective combination of options. In particular, HVAC equipment must be developed that addresses the range of special needs of NZEH applications in the areas of reduced HVAC and water heating energy use, humidity control, ventilation, uniform comfort, and ease of zoning. In FY05 ORNL conducted an initial Stage 1 (Applied Research) scoping assessment of HVAC/WH systems options for future NZEHs to help DOE/BT identify and prioritize alternative approaches for further development. Eleven system concepts with central air distribution ducting and nine multi-zone systems were selected and their annual and peak demand performance estimated for five locations: Atlanta (mixed-humid), Houston (hot-humid), Phoenix (hot-dry), San Francisco (marine), and Chicago (cold). Performance was estimated by simulating the systems using the TRNSYS simulation engine (Solar Energy Laboratory et al. 2006) in two 1800-ft{sup 2} houses--a Building America (BA) benchmark house and a prototype NZEH taken from BEopt results at the take-off (or crossover) point (i.e., a house incorporating those design features such that further progress towards ZEH is through the addition of photovoltaic power sources, as determined by current BEopt analyses conducted by NREL). Results were summarized in a project report, 'HVAC Equipment Design options for Near-Zero-Energy Homes--A Stage 2 Scoping Assessment', ORNL/TM-2005/194 (Baxter 2005). The 2005 study report describes the HVAC options considered, the ranking criteria used, and the system rankings by priority. Table 1 summarizes the energy savings potential of the highest scoring options from the 2005 study for all five locations. All system options were scored by the ORNL building equipment research team and by William Goetzler of Navigant Consulting. These scores were reviewed by DOE/BT's Residential Integration program leaders and Building America team members. Based on these results, the two centrally ducted integrated heat pump (IHP) systems (air source and ground source versions) were selected for advancement to Stage 2 (Exploratory Development) business case assessments in FY06. This report describes results of these business case assessments. It is a compilation of three separate reports describing the initial business case study (Baxter 2006a), an update to evaluate the impact of an economizer cooling option (Baxter 2006b), and a second update to evaluate the impact of a winter humidification option (Baxter 2007). In addition it reports some corrections made subsequent to release of the first two reports to correct some errors in the TRNSYS building model for Atlanta and in the refrigerant pressure drop calculation in the water-to-refrigerant evaporator module of the ORNL Heat Pump Design Model (HPDM) used for the IHP analyses. These changes resulted in some minor differences between IHP performance as reported in Baxter (2006a, b) and in this report

Initial Business Case Analysis of Two Integrated Heat Pump HVAC Systems for Near-Zero-Energy Homes -- Update to Include Analyses of an Economizer Option and Alternative Winter Water Heating Control Option

The long range strategic goal of the Department of Energy's Building Technologies (DOE/BT) Program is to create, by 2020, technologies and design approaches that enable the construction of net-zero energy homes at low incremental cost (DOE/BT 2005). A net zero energy home (NZEH) is a residential building with greatly reduced needs for energy through efficiency gains, with the balance of energy needs supplied by renewable technologies. While initially focused on new construction, these technologies and design approaches are intended to have application to buildings constructed before 2020 as well resulting in substantial reduction in energy use for all building types and ages. DOE/BT's Emerging Technologies (ET) team is working to support this strategic goal by identifying and developing advanced heating, ventilating, air-conditioning, and water heating (HVAC/WH) technology options applicable to NZEHs. Although the energy efficiency of heating, ventilating, and air-conditioning (HVAC) equipment has increased substantially in recent years, new approaches are needed to continue this trend. Dramatic efficiency improvements are necessary to enable progress toward the NZEH goals, and will require a radical rethinking of opportunities to improve system performance. The large reductions in HVAC energy consumption necessary to support the NZEH goals require a systems-oriented analysis approach that characterizes each element of energy consumption, identifies alternatives, and determines the most cost-effective combination of options. In particular, HVAC equipment must be developed that addresses the range of special needs of NZEH applications in the areas of reduced HVAC and water heating energy use, humidity control, ventilation, uniform comfort, and ease of zoning. In FY05 ORNL conducted an initial Stage 1 (Applied Research) scoping assessment of HVAC/WH systems options for future NZEHs to help DOE/BT identify and prioritize alternative approaches for further development. Eleven system concepts with central air distribution ducting and nine multi-zone systems were selected and their annual and peak demand performance estimated for five locations: Atlanta (mixed-humid), Houston (hot-humid), Phoenix (hot-dry), San Francisco (marine), and Chicago (cold). Performance was estimated by simulating the systems using the TRNSYS simulation engine (Solar Energy Laboratory et al. 2006) in two 1800-ft{sup 2} houses--a Building America (BA) benchmark house and a prototype NZEH taken from BEopt results at the take-off (or crossover) point (i.e., a house incorporating those design features such that further progress towards ZEH is through the addition of photovoltaic power sources, as determined by current BEopt analyses conducted by NREL). Results were summarized in a project report, HVAC Equipment Design options for Near-Zero-Energy Homes--A Stage 2 Scoping Assessment, ORNL/TM-2005/194 (Baxter 2005). The 2005 study report describes the HVAC options considered, the ranking criteria used, and the system rankings by priority. In 2006, the two top-ranked options from the 2005 study, air-source and ground-source versions of an integrated heat pump (IHP) system, were subjected to an initial business case study. The IHPs were subjected to a more rigorous hourly-based assessment of their performance potential compared to a baseline suite of equipment of legally minimum efficiency that provided the same heating, cooling, water heating, demand dehumidification, and ventilation services as the IHPs. Results were summarized in a project report, Initial Business Case Analysis of Two Integrated Heat Pump HVAC Systems for Near-Zero-Energy Homes, ORNL/TM-2006/130 (Baxter 2006). The present report is an update to that document. Its primary purpose is to summarize results of an analysis of the potential of adding an outdoor air economizer operating mode to the IHPs to take advantage of free cooling (using outdoor air to cool the house) whenever possible. In addition it provides some additional detail for an alternative winter water heating/space heating (WH/SH) control strategy briefly described in the original report and corrects some minor errors

HVAC Equipment Design Options for Near-Zero-Energy Homes (NZEH) -A Stage 2 Scoping Assessment

Although the energy efficiency of heating, ventilating, and air-conditioning (HVAC) equipment has increased substantially in recent years, new approaches are needed to continue this trend. Conventional unitary equipment and system designs have matured to a point where cost-effective, dramatic efficiency improvements that meet near-zero-energy housing (NZEH) goals require a radical rethinking of opportunities to improve system performance. The large reductions in HVAC energy consumption necessary to support the NZEH goals require a systems-oriented analysis approach that characterizes each element of energy consumption, identifies alternatives, and determines the most cost-effective combination of options. In particular, HVAC equipment must be developed that addresses the range of special needs of NZEH applications in the areas of reduced HVAC and water heating energy use, humidity control, ventilation, uniform comfort, and ease of zoning. This report describes results of a scoping assessment of HVAC system options for NZEH homes. ORNL has completed a preliminary adaptation, for consideration by The U.S. Department of Energy, Energy Efficiency and Renewable Energy Office, Building Technologies (BT) Program, of Cooper's (2001) stage and gate planning process to the HVAC and Water Heating element of BT's multi-year plan, as illustrated in Figure 1. In order to adapt to R&D the Cooper process, which is focused on product development, and to keep the technology development process consistent with an appropriate role for the federal government, the number and content of the stages and gates needed to be modified. The potential federal role in technology development involves 6 stages and 7 gates, but depending on the nature and status of the concept, some or all of the responsibilities can flow to the private sector for product development beginning as early as Gate 3. In the proposed new technology development stage and gate sequence, the Stage 2 'Scoping Assessment' provides the deliverable leading into the Gate 3 'Scoping Assessment Screen'. This report is an example of a Stage 2 deliverable written to document the screening of options against the Gate 3 criteria and to support DOE decision making and option prioritization. The objective of this scoping assessment was to perform a transparent evaluation of the HVAC system options for NZEH based on the applying the Gate 3 criteria uniformly to all options

Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem

We prove that the $q$-state Potts antiferromagnet on a lattice of maximum coordination number $r$ exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever $q > 2r$. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for $q \ge 7$), triangular lattice ($q \ge 11$), hexagonal lattice ($q \ge 4$), and Kagom\'e lattice ($q \ge 6$). The proofs are based on the Dobrushin uniqueness theorem.Comment: 32 pages including 3 figures. Self-unpacking file containing the tex file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 ps file

Experimental Evaluation of High Performance Integrated Heat Pump

Integrated heat pump (IHP) technology provides significant potential for energy savings and comfort improvement for residential buildings. In this study, we evaluate the performance of a high performance IHP that provides space heating, cooling, and water heating services. Experiments were conducted according to the ASHRAE Standard 206-2013 where 24 test conditions were identified in order to evaluate the IHP performance indices. An 8-in by 8-in Air Monitor Fan Evaluator is used to measure the volumetric flowrate of air discharged from the air handler unit (AHU) in order to evaluate the airside performance. Empirical curve fits of the unit’s compressor maps are used in conjunction with saturated condensing and evaporating refrigerant conditions to deduce the refrigerant mass flowrate, which, in turn is used to evaluate the refrigerant-side performance. Heat pump (compressor, fans, and controls) and water pump power were measured separately per requirements of Standard 206. The system was charged per the system manufacturer’s specifications. System test results are presented for each operating mode along with overall IHP performance metrics according to ASHRAE standard 206-2013. The paper ends with discussion on system operation and impact on typical energy consumption in residential buildings

Three-phase point in a binary hard-core lattice model?

Using Monte Carlo simulation, Van Duijneveldt and Lekkerkerker [Phys. Rev. Lett. 71, 4264 (1993)] found gas-liquid-solid behaviour in a simple two-dimensional lattice model with two types of hard particles. The same model is studied here by means of numerical transfer matrix calculations, focusing on the finite size scaling of the gaps between the largest few eigenvalues. No evidence for a gas-liquid transition is found. We discuss the relation of the model with a solvable RSOS model of which the states obey the same exclusion rules. Finally, a detailed analysis of the relation with the dilute three-state Potts model strongly supports the tricritical point rather than a three-phase point.Comment: 17 pages, LaTeX2e, 13 EPS figure

A classification of four-state spin edge Potts models

We classify four-state spin models with interactions along the edges according to their behavior under a specific group of symmetry transformations. This analysis uses the measure of complexity of the action of the symmetries, in the spirit of the study of discrete dynamical systems on the space of parameters of the models, and aims at uncovering solvable ones. We find that the action of these symmetries has low complexity (polynomial growth, zero entropy). We obtain natural parametrizations of various models, among which an unexpected elliptic parametrization of the four-state chiral Potts model, which we use to localize possible integrability conditions associated with high genus curves.Comment: 5 figure

Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type

A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order) or smooth (continuous). In addition there are tricritical points where a smooth boundary changes into a sharp one and triple points where three sharp boundaries meet. Finally our numerical results strongly suggest the existence of conical points, at which tangent planes of a finite range of orientations all intersect each other. The thermal evolution of the equilibrium shape in this model shows strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include

Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution $\eta$ and $q=N_H/N_C$, the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of $q$, for $q \gg 1$ and $q \lesssim 1$ respectively.Comment: 5 figure