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The phase separation behavior of poly(vinyl methyl ether)/polystyrene semi-IPN/
The effect of crosslinking on the phase stability and phase separation behavior of poly(vinyl methyl ether)/polystyrene semi-IPN was studied by light scattering. The cloud point temperature was measured as a function of degree of crosslinking and found to be constant within experimental precision. The result of this experiment was combined with a theoretical prediction of the phase diagram to determine conditions for the following experiment. Wide angle light scattering was used to quantitatively analyze the mechanism and dynamics of the thermally induced phase separation with respect to the crosslinking density and the thermal condition. An apparatus with a one dimensional diode array was used to simultaneously monitor a wide range of scattering angles. Analysis of the early stages of phase separation indicates that the spinodal temperature remained virtually constant whether or not crosslinks were present in the system. This was demonstrated to be consistent with theoretical prediction. However, the apparent diffusion coefficient decreased dramatically with the introduction of crosslinks thus the initial phase separation was slowed down significantly. The final scattering intensity was shown to decrease with increasing crosslinking density. The scattering vector dependence of the scattering intensity was negligible compared with its overall time dependence. A plateau region was observed for some of the scattering intensity data of the semi-IPN systems with respect to time. This indicates that the crosslinks restrict terminal phase contrast and not the size of phase
Optical Evidence of Itinerant-Localized Crossover of Electrons in Cerium Compounds
Cerium (Ce)-based heavy-fermion materials have a characteristic double-peak
structure (mid-IR peak) in the optical conductivity [] spectra
originating from the strong conduction ()-- electron hybridization. To
clarify the behavior of the mid-IR peak at a low - hybridization
strength, we compared the spectra of the isostructural
antiferromagnetic and heavy-fermion Ce compounds with the calculated unoccupied
density of states and the spectra obtained from the impurity Anderson model.
With decreasing - hybridization intensity, the mid-IR peak shifts to the
low-energy side owing to the renormalization of the unoccupied state, but
suddenly shifts to the high-energy side owing to the - on-site Coulomb
interaction at a slight localized side from the quantum critical point (QCP).
This finding gives us information on the change in the electronic structure
across QCP.Comment: 6 pages, 4 figures. To appear in JPSJ (Letters
Little IIB Matrix Model
We study the zero-dimensional reduced model of D=6 pure super Yang-Mills
theory and argue that the large N limit describes the (2,0) Little String
Theory. The one-loop effective action shows that the force exerted between two
diagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional
spacetime. We also observe that it is due to non-gravitational interactions. We
construct wave functions and vertex operators which realize the D=6, (2,0)
tensor representation. We also comment on other "little" analogues of the IIB
matrix model and Matrix Theory with less supercharges.Comment: 17 pages, references adde
Fans and polytopes in tilting theory II: -fans of rank 2
The -fan of a finite dimensional algebra is a fan in its real Grothendieck
group defined by tilting theory. We give a classification of complete -fans
of rank 2. More explicitly, our first main result asserts that every complete
sign-coherent fan of rank 2 is a -fan of some finite dimensional algebra.
Our proof is based on three fundamental results, Gluing Theorem, Rotation
Theorem and Subdivision Theorem, which realize basic operations on fans in the
level of finite dimensional algebras. For each of 16 convex sign-coherent fans
of rank 2, our second main result gives a characterization of algebras
of rank 2 satisfying . As a by-product of our method, we
prove that for each positive integer , there exists a finite dimensional
algebra of rank 2 such that the Hasse quiver of the poset of 2-term silting
complexes of has precisely connected components.Comment: 37 pages, v2: Fixed typos, updated references and added section
Fans and polytopes in tilting theory
For a finite dimensional algebra over a field , the 2-term silting
complexes of gives a simplicial complex called the
-simplicial complex. We give tilting theoretic interpretations of the
-vectors and Dehn-Sommerville equations of . Using -vectors of
2-term silting complexes, gives a nonsingular fan in
the real Grothendieck group called the
-fan. For example, the fan of -vectors of a cluster algebra is given by
the -fan of a Jacobian algebra of a non-degenerate quiver with potential. We
give several properties of including idempotent reductions,
sign-coherence, Jasso reductions and a connection with Newton polytopes of
-modules. Moreover, gives a (possibly infinite and non-convex)
polytope in called the -polytope
of . We call -convex if is convex. In this case, we show that
it is a reflexive polytope, and that the dual polytope is given by the 2-term
simple minded collections of .
We give an explicit classification of -convex algebras of rank . We
classify algebras whose -polytopes are smooth Fano. We classify classical
and generalized preprojective algebras which are -convex, and also describe
their -polytope as the dual polytopes of short root polytopes of type
and . We also classify Brauer graph algebras which are -convex, and
describe their -polytopes as root polytopes of type and .Comment: 70 page
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