EXPERIMENTAL INVESTIGATION OF THE INFLUENCE OF MULTI-RECYCLING ON THE FRACTURE BEHAVIOR OF POST CONSUMER HIGH IMPACT POLYSTYRENE FROM DISPOSABLE CUPS EVALUATED BY THE J-INTEGRAL APPROACH.

The aim of the present paper is to study the effect of multi-recycling on the fracture behavior of high impact polystyrene from disposable cups. After collecting and washing the material, it was subjected to six cycles of recycling. After each cycle, it was subjected to tensile tests to determine the R-curves. The theory of the J-integral contour has been used for the development of a characterization method of the fracture strength appropriate to the case of this non-linear elastoplastic polymer material. To this end, the method of multiple specimens (Single edge notch tension SENT) of thin thickness was used, by introducing cracks of the same lengths to several identical test pieces. The results suggested a slight decrease in crack resistance of recycled high impact polystyrene, especially during the first cycle, demonstrated by a comparison of JIC values related to initiation of crack propagation. The fracture energy absorbed as a function of the cycles suggested a weakening within the material. ABSTRAK: Tujuan kajian ini adalah bagi mengkaji kesan tindak balas pada pelbagai peringkat-kitar semula ke atas kerapuhan polisterin berimpak tinggi pada cawan pakai buang. Selepas mengumpul dan membasuh cawan ini, terdapat enam peringkat kitar semula. Pada setiap peringkat, ianya akan melalui ujian tegangan bagi mendapatkan lengkung-R. Teori kamiran-J kontur telah digunakan bagi mencipta kaedah khas bagi mengkaji kekuatan retakan bersesuaian bagi kes bahan polimer elastoplastik yang tidak-linear. Sehingga kini, kaedah Regangan Tepi Takuk Tunggal (SENT) telah digunakan pada spesimen berketebalan rendah, dengan menghasilkan keretakan sama panjang di permulaan kajian di buat pada pelbagai bahan uji yang serupa. Dapatan kajian menunjukkan rintangan pada retakan telah berkurang sedikit pada polisterin kitar semula berimpak tinggi, terutama pada kitaran pertama, yang ditunjukkan pada nilai JIC pada permukaan rambatan retakan awal. Tenaga kerapuhan yang meresap pada setiap kitaran menunjukkan bahan telah melemah dari dalam.

Eigenbranes in Jackiw-Teitelboim gravity

It was proven recently that JT gravity can be defined as an ensemble of L × L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with 1 ≪ N ≪ L eigenvalues held fixed. This corresponds to a version of JT gravity which includes N FZZT type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.

Partial and Local Argument Properties of Holomorphic and Meromorphic Complex Functions in Several Variables

The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply n-variable complex functions with n≥2. Argument analytic relationships for n-variable complex functions with significance similar to the argument principle for one-variable ones are retrieved partially and locally. More precisely, argument analysis in n-variable complex functions is carried out one-by-one in terms of each and all variables, namely, partially, so that argument-principle-like relations are established in poly-disc neighborhoods of the variable domains, namely locally. The technique is applicable graphically with loci plotting, independent of Cauchy integral contour and locus orientations; it is also numerically tractable without loci plotting via argument incremental integration. Numerical examples are included to illustrate the main results.

Classification of out-of-time-order correlators

The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n\leq 4n≤4) to exemplify the general statements.