Studying anomalous scaling and heat transport of turbulent thermal convection using a dynamical model

Turbulent thermal convection is a well-studied problem with various issues of interest. In this paper, we review our work which shows the nature and origin of anomalous scaling and heat transport in the limit of very strong thermal forcing, can be gained by studying a dynamical model, known as shell model, of homogeneous turbulent thermal convection in which buoyancy acts directly at most scales. Specifically, we have obtained two results. The first result is that when buoyancy acts directly at most scales such that the dynamics are governed by a cascade of entropy, the scaling behavior is described by Bolgiano and Obukhov scaling plus corrections that are due to the variations of the local entropy transfer rate. This result indicates the validity of the extension of refined similarity hypothesis to turbulent thermal convection. The second result is that when buoyancy is acting directly at most scales, a damping term acting on the largest scale, which has to be added for the system to achieve stationarity, plays a crucial role in heat transport, and that the heat transport depends on the strength of thermal forcing in the same manner as that predicted for the ultimate state of very strong thermal forcing. With our interpretation of the damping term representing the effect of the boundaries, this result indicates that in the ultimate state of turbulent thermal convection, when buoyancy is acting at most scales, boundaries would play a significant role in heat transport.     

A new approach for the large-scale generation of mature dendritic cells from adherent PBMC using roller bottle technology

Background  

Human monocyte-derived DC (mDC) loaded with peptides, protein, tumor cell lysates, or tumor cell RNA, are being tested as vaccines against multiple human malignancies and viral infection with great promise. One of the factors that has limited more widespread use of these vaccines is the need to generate mDC in large scale. Current methods for the large-scale cultivation of mDC in static culture vessels are labor- and time- intensive, and also require many culture vessels. Here, we describe a new method for the large-scale generation of human mDC from human PBMC from leukopheresis or buffy coat products using roller bottles, never attempted before for mDC generation. We have tested this technology using 850 cm² roller bottles compared to conventional T-175 flat-bottom static culture flasks.     

Investigation of host-to-activator energy transfer and surface losses in SrY2O4:Eu under VUV excitation

We have completed a study of the optical properties of SrY₂O₄:Eu³⁺ under vacuum ultraviolet (VUV) excitation. Reflectance measurements on the undoped material yield a calculated band gap of about 6.1 eV. Studies on the doped material indicate that Eu³⁺ occupies the Y(1) and Y(2) sites in this host. Host-to-activator energy transfer calculations indicate a preference for transfer to Eu³⁺ at the Y(2) site. Modeling of the transfer efficiency data leads us to estimate that about 35% of absorbed radiation is lost to the surface under excitation near the band edge.     

On the noise sensitivity of monotone functions

It is known that for all monotone functions f : {0, 1}ⁿ → {0, 1}, if x ∈ {0, 1}ⁿ is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ? = n^?α, then P[f(x) ≠ f(y)] < cn^?α+1/2, for some c > 0. Previously, the best construction of monotone functions satisfying P[f_n(x) ≠ f_n(y)] ≥ δ, where 0 < δ < 1/2, required ? ≥ c(δ)n^?α, where α = 1 ? ln 2/ln 3 = 0.36907 …, and c(δ) > 0. We improve this result by achieving for every 0 < δ < 1/2, P[f_n(x) ≠ f_n(y)] ≥ δ, with:

• ? = c(δ)n^?α for any α < 1/2, using the recursive majority function with arity k = k(α);
• ? = c(δ)n^?1/2log^tn for t = log₂ = .3257 …, using an explicit recursive majority function with increasing arities; and
• ? = c(δ)n^?1/2, nonconstructively, following a probabilistic CNF construction due to Talagrand.

We also study the problem of achieving the best dependence on δ in the case that the noise rate ? is at least a small constant; the results we obtain are tight to within logarithmic factors. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 333–350, 2003     

Looking for Difference Sets in Groups with Dihedral Images

We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a + 2 for a unique choice of = ±1, and for a = (k – )/2p. If G has an image of order 2p, then and ( – 1)/( – 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D _2m with either (n, m) = 1 or m = p ^t for p an odd prime dividing n, then one of the C ₂ intersection numbers of D is divisible by m. Again, this gives some non-existence results.     

A sharp bound for the degree of proper monomial mappings between balls

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.     

A lower bound for the optimal crossing-free Hamiltonian cycle problem

Consider a drawing in the plane ofK _n , the complete graph onn vertices. If all edges are restricted to be straight line segments, the drawing is called rectilinear. Consider a Hamiltonian cycle in a drawing ofK _n . If no pair of the edges of the cycle cross, it is called a crossing-free Hamiltonian cycle (cfhc). Let (n) represent the maximum number of cfhc's of any drawing ofK _n , and (n) the maximum number of cfhc's of any rectilinear drawing ofK _n . The problem of determining (n) and (n), and determining which drawings have this many cfhc's, is known as the optimal cfhc problem. We present a brief survey of recent work on this problem, and then, employing a recursive counting argument based on computer enumeration, we establish a substantially improved lower bound for (n) and (n). In particular, it is shown that (n) is at leastk × 3.2684 ⁿ . We conjecture that both (n) and (n) are at mostc × 4.5 ⁿ .This research, part of which was conducted at Queen's University, was supported by an N.S.E.R.C. postgraduate scholarship.     

Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms

The cooperative luminescence and absorption properties of Yb³⁺ doped aluminosilicate glass optical fibres and preforms are investigated in detail. In accordance with previous investigations, both the visible cooperative luminescence and the infrared luminescence decay measurements have been resolved into a single exponential decay component. We show that for a glass with similar Yb³⁺ dopant concentration but more Al³⁺, the glass emits less visible luminescence. Absorption loss measurements completed on fibre samples revealed a broad absorption in the 350-500 nm range, which we propose is due to a combination of Yb²⁺ absorption and cooperative absorption from Yb³⁺ ion pairs.     

Local spin correlations in partially frustrated amorphous Fe-Mn

Mössbauer measurements in a-(Fe_0.765Mn_0.235)₇₈Sn₂Si₆B₁₄ have been performed with⁵⁷Fe and¹¹⁹Sn. Both hyperfine fields show a kink near 70 K, indicating a freezing of the transverse spins. The ratio of the two hyperfine fields contains information about the correlation of the transverse spins. The ratioB _hf(Sn)/B _hf(Fe) stays constant aboveT _xy and rises belowT _xy . This indicates an alignment of the transverse spins on a local scale, as was also found inAuFe and a-FeZr.