Algebraic Aspects of Abelian Sandpile Models

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G, and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of toppling matrix. We construct scalar functions, linear in height variables of the pile, that are invariant toppling at any site. These invariants provide convenient coordinates to label the recurrent configurations of the sandpile. For an L X L square lattice, we show that g = L. In this case, we observe that the system has nontrivial symmetries coming from the action of the cyclotomic Galois group of the (2L+2)th roots of unity which operates on the set of eigenvalues of the toppling matrix. These eigenvalues are algebraic integers, whose product is the order |G|. With the help of this Galois group, we obtain an explicit factorizaration of |G|. We also use it to define other simpler, though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3

Demonstration of Einstein-Podolsky-Rosen Steering Using Hybrid Continuous- and Discrete-Variable Entanglement of Light

Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided device-independent quantum information protocols. Here we demonstrate steering using hybrid entanglement between continuous- and discrete-variable optical qubits. To this end, we report on suitable steering inequalities and detail the implementation and requirements for this demonstration. Steering is experimentally certified by observing a violation by more than 5 standard deviations. Our results illustrate the potential of optical hybrid entanglement for applications in heterogeneous quantum networks that would interconnect disparate physical platforms and encodings

The effects of chest wall loading on perceptions of fatigue, exercise performance, pulmonary function, and muscle perfusion.

BACKGROUND: Load carriage (LC), which directly affects the chest wall and locomotor muscles, has been suggested to alter the ventilatory and circulatory responses to exercise, leading to increased respiratory muscle work and fatigue. However, studies exploring the impact of LC on locomotion increased internal work, complicating their interpretation. To overcome this issue, we sought to determine the effect of chest wall loading with restriction (CWL + R) on cycling performance, cardiopulmonary responses, microvascular responsiveness, and perceptions of fatigue. METHODS: In a randomized crossover design, 23 young healthy males (22 \ub1 4 years) completed a 5 km cycling time trial (TT) in loaded (CWL + R; tightened vest with 10% body weight) and unloaded conditions. After baseline pulmonary function testing (PFT; forced expiratory volume in 1 s, FEV1; forced vital capacity, FVC), cardiopulmonary indices (HR, heart rate; O2 uptake, VO2; ventilation, VE; tidal volume, VT; and breathing frequency, Bf), rating of perceived exertion (RPE), lactate (BLa), and microvascular responses (oxy-, deoxy-, total hemoglobin; and tissue saturation; StO2) of the vastus lateralis using near infrared spectroscopy were collected during the TT; and PFT was repeated post-exercise. RESULTS: Pre-exercise, CWL + R reduced (p < 0.05) FVC (5.6 \ub1 0.8 versus 5.5 \ub1 0.7 L), FEV1 (4.8 \ub1 0.7 versus 4.7 \ub1 0.6 L), and FEV1/FVC (0.9 \ub1 0.1 versus 0.8 \ub1 0.1). CWL + R modified power output (PO) over time (interaction, p = 0.02), although the 5 km time (461 \ub1 24 versus 470 \ub1 27 seconds), VT (3.0 \ub1 0.3 versus 2.8 \ub1 0.8 L), Bf, VE, HR, VO2, microvascular and perceptual (visual analog scale, or VAS, and RPE) responses were unchanged (p > 0.05). CWL + R increased (p < 0.05) the average BLa (7.6 \ub1 2.6 versus 8.6 \ub1 3 mmol/L). CONCLUSIONS: Modest CWL + R negatively affects pre-exercise pulmonary function, modifies cycling power output over time, and increases lactate production during a 5 km cycling trial, although the cardiorespiratory, microvascular, and perceptual responses were unaffected

Birefringence analysis of multilayer leaky cladding optical fibre

We analyse a multilayer leaky cladding (MLC) fibre using the finite element method and study the effect of the MLC on the bending loss and birefringence of two types of structures: (i) a circular core large-mode-area structure and (ii) an elliptical-small-core structure. In a large-mode-area structure, we verify that the multilayer leaky cladding strongly discriminates against higher order modes to achieve single-mode operation, the fibre shows negligible birefringence, and the bending loss of the fibre is low for bending radii larger than 10 cm. In the elliptical-small-core structure we show that the MLC reduces the birefringence of the fibre. This prevents the structure from becoming birefringent in case of any departures from circular geometry. The study should be useful in the designs of MLC fibres for various applications including high power amplifiers, gain flattening of fibre amplifiers and dispersion compensation.Comment: 18 page