Ergodicity versus non-ergodicity for Probabilistic Cellular Automata on rooted trees

In this article we study a class of shift-invariant and positive rate probabilistic cellular automata (PCA) on rooted d-regular trees $\mathbb{T}^d$. In a first result we extend the results of [10] on trees, namely we prove that to every stationary measure $\nu$ of the PCA we can associate a space-time Gibbs measure $\mu_{\nu}$ on $\mathbb{Z} \times \mathbb{T}^d$. Under certain assumptions on the dynamics the converse is also true. A second result concerns proving sufficient conditions for ergodicity and non-ergodicity of our PCA on d-ary trees for $d\in \{ 1,2,3\}$ and characterizing the invariant product Bernoulli measures.Comment: 17 page

Chemical Pressure Effect on the Magnetic Order of the La1.4Sr1.6Mn2O7 Bilayered Manganite

In this Communication is it shown the role of Ca-doping in stabilizing the A-type AFM structure of the optimally doped La1.4Sr1.6Mn2O7 bilayered manganite.Comment: 10 pages, 4 figure

Nucleation for one-dimensional long-range Ising models

In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory with two examples (exponentially and polynomially decaying interaction) and we show that the critical droplet can be macroscopic or mesoscopic, according to the value of the external magnetic field.Comment: 15 pages, 3 figure

Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields

We consider ferromagnetic long-range Ising models which display phase transitions. They are long-range one-dimensional Ising ferromagnets, in which the interaction is given by $J_{x,y} = J(|x-y|)\equiv \frac{1}{|x-y|^{2-\alpha}}$ with $\alpha \in [0, 1)$, in particular, $J(1)=1$. For this class of models one way in which one can prove the phase transition is via a kind of Peierls contour argument, using the adaptation of the Fr\"ohlich-Spencer contours for $\alpha \neq 0$, proposed by Cassandro, Ferrari, Merola and Presutti. As proved by Fr\"ohlich and Spencer for $\alpha=0$ and conjectured by Cassandro et al for the region they could treat, $\alpha \in (0,\alpha_{+})$ for $\alpha_+=\log(3)/\log(2)-1$, although in the literature dealing with contour methods for these models it is generally assumed that $J(1)\gg1$, we can show that this condition can be removed in the contour analysis. In addition, combining our theorem with a recent result of Littin and Picco we prove the persistence of the contour proof of the phase transition for any $\alpha \in [0,1)$. Moreover, we show that when we add a magnetic field decaying to zero, given by $h_x= h_*\cdot(1+|x|)^{-\gamma}$ and $\gamma >\max\{1-\alpha, 1-\alpha^* \}$ where $\alpha^*\approx 0.2714$, the transition still persists.Comment: 13 page

Experimental and Theoretical Analysis of Subcooling Control in Residential Air Conditioning Systems

Widespread use of electronic expansion valves in residential air conditioning systems has provided an opportunity to further improve performance by use of alternative refrigerant flow control strategies. This paper focuses on an experimental and theoretical investigation on the effect of subcooling control in air conditioning system. A 2 Ton (7 kW) R410-A system was used in the experimental study and a model for the same system was developed and validated. The paper provides a theoretical analysis and determination of a control scheme to maximize COP and an experimental validation on the performance of a RAC system with subcooling control against a TXV-based baseline system. The theoretical analysis showed that subcooling can be defined as a linear function of temperature difference of refrigerant condensation and condenser air (����������������) and that the effect of the evaporator conditions on its COP-maximizing values are negligible. The system was evaluated at AHRI 240/270 dry conditions with a properly charged TXV (6600g) and EXV subcooling control (8500g) comparison. Results show an average 9.8% increase in COP and 10.4% in capacity using subcooling control for the SEER conditions and a resulting increase of 9.4% in SEER. Validation with both experimental and model data show that subcooling control based on ���������������� prov ides a co nt rol sche me with good agreement to the data for air conditioning system capable of increasing both COP and capacity

Effect of Subcooling Control on Residential Heat Pump Systems’ Performance

An electronic expansion valve can be used to improve efficiency and capacity in residential heat pump system by changing the focus of its control method on condenser subcooling and allowing slightly wet compressor suction to reduce discharge temperatures. This paper will present results of an experimental and theoretical analysis of the use of subcooling control. An investigation based on ideal cycle analysis shows potential improvements in HPF can be obtained if the subcooling is controlled by the system’s expansion valve, but higher specific heating capacity and pressure ratios may reduce the overall improvement as outdoor temperatures are further decreased. A 2-Ton (7 kW) off-the-shelf residential system was used to evaluate the effect of subcooling control the system’s performance characteristics under a range of external conditions for HSPF calculation and compared with the original system’s expansion control. HPF (Heating performance factor) was increased by up to 19.1% in low load conditions and up to 4.2% in high load conditions. Heating capacity was also improved by up to 18.1%, which penalizes low load conditions by requiring more often on/off cycling but could lead to even higher HPF increase if the compressor speed is lowered to match the load of the residence in higher load conditions and can also improve efficiency at conditions that require auxiliary heating. HSPF was calculated for both subcooling controlled and baseline system showing an improvement of 19.2% in HSPF with a negative effect only observed between 0C and 5.5C which suffer from higher cycling degradation. The control scheme was defined as a linear function of the refrigerant condensation and indoor air inlet temperature difference. The control curve showed good agreement with both experimental and model data for the system, with the charge compensator causing some deviation from the rest of the data. The use of an accumulator as a charge receiver may eliminate the requirement of a charge compensator simplifying the cycle architecture while still providing an increase in efficiency with subcooling control