38,131 research outputs found
Dark energy imprints on the kinematic Sunyaev-Zel'dovich signal
We investigate the imprint of dark energy on the kinetic Sunyaev-Zel'dovich
(kSZ) angular power spectrum on scales of to , and find that
the kSZ signal is sensitive to the dark energy parameter. For example, varying
the constant by 20\% around results in a change on the
kSZ spectrum; changing the dark energy dynamics parametrized by by
, a 30\% change on the kSZ spectrum is expected. We discuss the
observational aspects and develop a fitting formula for the kSZ power spectrum.
Finally, we discuss how the precise modeling of the post-reionization signal
would help the constraints on patchy reionization signal, which is crucial for
measuring the duration of reionization.Comment: 12 pages, 9 figures, 2 table
Counting hypergraph matchings up to uniqueness threshold
We study the problem of approximately counting matchings in hypergraphs of
bounded maximum degree and maximum size of hyperedges. With an activity
parameter , each matching is assigned a weight .
The counting problem is formulated as computing a partition function that gives
the sum of the weights of all matchings in a hypergraph. This problem unifies
two extensively studied statistical physics models in approximate counting: the
hardcore model (graph independent sets) and the monomer-dimer model (graph
matchings).
For this model, the critical activity
is the threshold for the uniqueness of Gibbs measures on the infinite
-uniform -regular hypertree. Consider hypergraphs of maximum
degree at most and maximum size of hyperedges at most . We show that
when , there is an FPTAS for computing the partition
function; and when , there is a PTAS for computing the
log-partition function. These algorithms are based on the decay of correlation
(strong spatial mixing) property of Gibbs distributions. When , there is no PRAS for the partition function or the log-partition
function unless NPRP.
Towards obtaining a sharp transition of computational complexity of
approximate counting, we study the local convergence from a sequence of finite
hypergraphs to the infinite lattice with specified symmetry. We show a
surprising connection between the local convergence and the reversibility of a
natural random walk. This leads us to a barrier for the hardness result: The
non-uniqueness of infinite Gibbs measure is not realizable by any finite
gadgets
Dilatancy relation for overconsolidated clay
A distinct feature of overconsolidated (OC) clays is that their dilatancy behavior is dependent on the degree of overconsolidation. Typically, a heavily OC clay shows volume expansion, whereas a lightly OC clay exhibits volume contraction when subjected to shear. Proper characterization of the stress-dilatancy behavior proves to be important for constitutive modeling of OC clays. This paper presents a dilatancy relation in conjunction with a bounding surface or subloading surface model to simulate the behavior of OC clays. At the same stress ratio, the proposed relation can reasonably capture the relatively more dilative response for clay with a higher overconsolidation ratio (OCR). It may recover to the dilatancy relation of a modified Cam-clay (MCC) model when the soil becomes normally consolidated (NC). A demonstrative example is shown by integrating the dilatancy relation into a bounding surface model. With only three extra parameters in addition to those in the MCC model, the new model and the proposed dilatancy relation provide good predictions on the behavior of OC clay compared with experimental data
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