Mineralogy and geochemistry of sulfide minerals and bulk rocks from ODP Hole 176-735B

Ocean Drilling Program (ODP) Leg 176 built upon the work of ODP Leg 118 wherein the 500-m section that was sampled represented the most complete recovery of an intact portion of lower oceanic crust ever described. During Leg 176, we deepened Hole 735B to >1500 m below seafloor in an environment where gabbroic rocks have been tectonically exposed at the Southwest Indian Ridge. This new expedition extended the remarkable recovery (>85%) that allowed unprecedented investigations into the nature of the lower oceanic crust as a result of Leg 118. Sulfide mineral and bulk rock compositions were determined from samples in the 1000-m section of oceanic gabbros recovered during Leg 176. The sulfide assemblage of pyrrhotite, chalcopyrite, pentlandite, and troilite is present throughout this section, as it is throughout the 500-m gabbroic section above that was sampled during Leg 118. Troilite is commonly present as lamellae, and the only interval where troilite was not observed is from the uppermost 150 m of the section sampled during Leg 118, which is intensely metamorphosed. The common presence of troilite indicates that much of the sulfide assemblage from Hole 735B precipitated from a magmatic system and subsequently underwent low-temperature reequilibration. Evaluation of geochemical trends in bulk rock and sulfides indicates that the combined effects of olivine accumulation in troctolites and high pentlandite to pyrrhotite ratios account for the sporadic bulk rock compositions high in Ni. Bulk rock and sulfide mineral geochemical indicators that are spatially coincident with structural and physical properties anomalies indicate a heretofore unrecognized lithologic unit boundary in this section. Platinum-group element (PGE) compositions were also determined for 36 samples from throughout the section that were recovered during Leg 176. Whereas most samples had low (<0.4 ppb) PGE concentrations, rare samples had elevated PGE values, but no unique common trend between these samples is evident.

Magnetic properties of ODP Hole 116-717C

Dark gray and black mud turbidites cored on ODP Leg 116 commonly yielded large magnetic susceptibility peaks. What is more, these peaks displayed different shapes suggesting variations in sedimentological processes. Consequently, a detailed study of the magnetic properties of two of these turbidites was undertaken to better understand the source of their unusual magnetism. Physical properties were measured as was the demagnetization behavior of sample natural remanent magnetizations (NRMs). Subsequently, an anhysteretic remanent magnetization (ARM) and saturation isothermal remanent magnetization (SIRM) were imparted to the samples, demagnetized, and various grain size tests based on the behavior of these remanences were applied. Finally, magnetic concentrates from two samples were examined with a scanning electron microscope with the capability to do energy dispersive X-ray (EDX) analysis. The turbidites stand out from surrounding layers because of their high susceptibilities, NRMs, ARMs, SIRMs, and ratios of ARM and SIRM to susceptibility. Their alternating field and thermal demagnetization properties and IRM acquisition curves are consistent with titanomagnetite grains as the primary magnetic mineral with some amount of hematite present. These properties are very similar to those published for samples from the Deccan flood basalts and suggest this formation as a possible source of the magnetic grains. Magnetic granulometry tests implied that the magnetic particles behave dominantly as single-domain and pseudo-single-domain grains. Moreover, they also implied that the large variation in susceptibility observed in the black mud turbidites results from a tenfold increase in the concentration of titanomagnetite grains. Electron microscope, EDX, and SIRM analyses revealed detrital titanomagnetites with typical sizes around 8-10 µm, but as large as 20-25 µm. These are probably the dominant magnetic grains in the black mud turbidites; however, ARM and susceptibility frequency-dependence suggested that there may also be a submicrometer fraction present. Most of the observed titanomagnetite grains are tabular and some display exsolution lamellae, accounting for the pseudo-single-domain behavior despite their moderate sizes. We hypothesize that the magnetic mineral concentration variations are brought about by sedimentological factors. The heavier magnetic minerals may tend to sink to the bottom of a turbidite; however, sometimes turbidite turbulence may act to keep these tabular, medium-size grains in suspension longer than some other larger or more equidimensional grains. Consequently, the susceptibility peak shape may reflect the turbidite current velocities as well as other sedimentological factors.

Chemistry of sulfide deposits from ODP Site 106-649

In Snake Pit massive sulfide fragments and friable, unconsolidated material recovered during ODP Leg 106, isocubanite and pyrite are generally the predominant phases, followed by marcasite, chalcopyrite, sphalerite, and pyrrhotite. Detailed analyses of paragenetic relations of minerals indicate that isocubanite first precipitated together with pyrrhotite. With decreasing temperature, chalcopyrite and sphalerite precipitated, and at the latest stage colloform sphalerite-pyrite (or colloform marcasite) formed. Isocubanite usually has exsolution lamellae of chalcopyrite and less commonly of pyrrhotite. The average bulk chemical composition of the friable, unconsolidated material indicates that it is rich in copper, reflecting the dominance of isocubanite in the specimens, and is characterized by high Co, low Pb, and Ag contents. Sulfur isotope ratios are very uniform, ranging in d34S from +1.2 to +2.8 per mil. The obtained values are apparently low, compared to those for the eastern Pacific sulfide samples, reflecting a smaller contribution of seawater sulfate in the Snake Pit sulfide deposit.

Representative analyses of pre-tectonic metabasic rocks and metapelitic gneiss from Sverdrupfjella, East Antarctica

Extensive high-grade polydeformed metamorphic provinces surrounding Archaean cratonic nuclei in the East Antarctic Shield record two tectono-thermal episodes in late Mesoproterozoic and late Neoproterozoic-Cambrian times. In Western Dronning Maud Land, the high-grade Mesoproterozoic Maud Belt is juxtaposed against the Archaean Grunehogna Province and has traditionally been interpreted as a Grenvillian mobile belt that was thermally overprinted during the Early Palaeozoic. Integration of new U-Pb sensitive high-resolution ion microprobe and conventional single zircon and monazite age data, and Ar-Ar data on hornblende and biotite, with thermobarometric calculations on rocks from the H.U. Sverdrupfjella, northern Maud Belt, resulted in a more complex P-T-t evolution than previously assumed. A c. 540?Ma monazite, hosted by an upper ampibolite-facies mineral assemblage defining a regionally dominant top-to-NW shear fabric, provides strong evidence for the penetrative deformation in the area being of Pan-African age and not of Grenvillian age as previously reported. Relics of an eclogite-facies garnet-omphacite assemblage within strain-protected mafic boudins indicate that the peak metamorphic conditions recorded by most rocks in the area (T = 687-758°C, P = 9·4-11·3?kbar) were attained subsequent to decompression from P > 12·9?kbar. By analogy with limited U-Pb single zircon age data and on circumstantial textural grounds, this earlier eclogite-facies metamorphism is ascribed to subduction and accretion around 565?Ma. Post-peak metamorphic K-metasomatism under amphibolite-facies conditions is ascribed to the intrusion of post-orogenic granite at c. 480?Ma. The recognition of extensive Pan-African tectonism in the Maud Belt casts doubts on previous Rodinia reconstructions, in which this belt takes a pivotal position between East Antarctica, the Kalahari Craton and Laurentia. Evidence of late Mesoproterozoic high-grade metamorphism during the formation of the Maud Belt exists in the form of c. 1035?Ma zircon overgrowths that are probably related to relics of granulite-facies metamorphism recorded from other parts of the Maud Belt. The polymetamorphic rocks are largely derived from a c. 1140?Ma volcanic arc and 1072 ± 10?Ma granite.

Magnetic properties and geochemistry in DSDP Holes 69-504B an d 69-505B

More than 60 basalt samples from two Deep Sea Drilling Project holes on the Costa Rica Rift were studied for magnetic properties and were found to have no properties significantly different from other DSDP basalts. Opaque mineralogical and thermomagnetic properties of these samples, however, to some extent show differences from normal submarine basalts; a new type of thermomagnetic curve and wide range of chemical compositions were recognized. Oxidized samples possibly containing incipient ilmenite exsolution lamellae were reduced and re-equilibrated during heating. The Curie temperatures of the re-equilibrated titanomagnetites are interpreted to be those of the original crystallized phase before oxidation.

Cuttlebone morphometry measurements

Changes in seawater carbonate chemistry that accompany ongoing ocean acidification have been found to affect calcification processes in many marine invertebrates. In contrast to the response of most invertebrates, calcification rates increase in the cephalopod Sepia officials during long-term exposure to elevated seawater pCO2. The present trial investigated structural changes in the cuttlebones of S. officinalis calcified during 6 weeks of exposure to 615 Pa CO2. Cuttlebone mass increased sevenfold over the course of the growth trail, reaching a mean value of 0.71 ± 0.15 g. Depending on cuttlefish size (mantle lengths 44-56 mm), cuttlebones of CO2-incubated individuals accreted 22-55% more CaCO3 compared to controls at 64 Pa CO2. However, the height of the CO2- exposed cuttlebones was reduced. A decrease in spacing of the cuttlebone lamellae, from 384 ± 26 to 195 ± 38 lm, accounted for the height reduction The greater CaCO3 content of the CO2-incubated cuttlebones can be attributed to an increase in thickness of the lamellar and pillar walls. Particularly, pillar thickness increased from 2.6 ± 0.6 to 4.9 ± 2.2 lm. Interestingly, the incorporation of non-acidsoluble organic matrix (chitin) in the cuttlebones of CO2- exposed individuals was reduced by 30% on average. The apparent robustness of calcification processes in S. officials, and other powerful ion regulators such as decapod cructaceans, during exposure to elevated pCO2 is predicated to be closely connected to the increased extracellular [HCO3 -] maintained by these organisms to compensate extracellular pH. The potential negative impact of increased calcification in the cuttlebone of S. officials is discussed with regard to its function as a lightweight and highly porous buoyancy regulation device. Further studies working with lower seawater pCO2 values are necessary to evaluate if the observed phenomenon is of ecological relevance.

Morphological descriptions from the recent bivalve of the genus Calyptogena (Vesicomyidae)

The genus Calyptogena (Bivalvia: Vesicomyidae) comprises highly specialized bivalves living in symbiosis with sulphur-oxidizing bacteria in reducing habitats. In this study, the genus is revised using shell and anatomical features. The work is based on type material, as well as on the extensive collection of vesicomyids obtained during twelve expeditions to the Pacific and Indian Oceans. Nine Recent species are ascribed to the genus Calyptogena, four of which are new: C. pacifica Dall, 1891, C. fausta Okutani, Fujikura & Hashimoto, 1993, C. rectimargo Scarlato, 1981, C. valdiviae (Thiele & Jaeckel, 1931), C. gallardoi Sellanes & Krylova, 2005, C. goffrediae n. sp., C. starobogatovi n. sp., C. makranensis n. sp. and C. costaricana n. sp. The characteristic features of Calyptogena are: shell up to 90 mm in length, elongate-elliptical or elongate; presence of escutcheon; presence of broad posterior ramus (3b) of right subumbonal cardinal tooth as well as right posterior nymphal ridge; absence of pallial sinus as a result of attachment of intersiphonal septal retractor immediately adjacent to ventral surface of posterior adductor; absence of processes on inner vulva of inhalant siphon; presence of inner demibranch only, with descending and ascending lamellae with interlamellar septa not divided into separate tubes. The most closely related taxa to Calyptogena are probably the genus Isorropodon Sturany, 1896, and the group of species represented by 'Calyptogena' phaseoliformis Métivier, Okutani & Ohta, 1986. These groups have several characters in common, namely absence of pallial sinus, presence of single inner pair of demibranchs and absence of processes on inner vulva of inhalant siphon. The worldwide distribution of the genus Calyptogena suggests that methane seeps at continental margins are the major dispersal routes and that speciation was promoted by geographical isolation. Recent species diversity and fossil records indicate that the genus originated in the Pacific Ocean. Sufficient data to discuss the distribution at species level exist only for C. pacifica, which has a remarkably narrow bathymetric range. Published studies on the physiology of C. pacifica suggest that adaptation to a specific geochemical environment has led to coexisting vesicomyid genera. The bacteria-containing gill of C. pacifica and other Calyptogena species is one of the most specialized in the family Vesicomyidae and may reflect these ecological adaptations.

Geochemistry of ocean floor and forearc serpentinites

We provide new insights into the geochemistry of serpentinites from mid-ocean ridges (Mid-Atlantic Ridge and Hess Deep), passive margins (Iberia Abyssal Plain and Newfoundland) and fore-arcs (Mariana and Guatemala) based on bulk-rock and in situ mineral major and trace element compositional data collected on drill cores from the Deep Sea Drilling Project and Ocean Drilling Program. These data are important for constraining the serpentinite-hosted trace element inventory of subduction zones. Bulk serpentinites show up to several orders of magnitude enrichments in Cl, B, Sr, U, Sb, Pb, Rb, Cs and Li relative to elements of similar compatibility during mantle melting, which correspond to the highest primitive mantle-normalized B/Nb, B/Th, U/Th, Sb/Ce, Sr/Nd and Li/Y among subducted lithologies of the oceanic lithosphere (serpentinites, sediments and altered igneous oceanic crust). Among the elements showing relative enrichment, Cl and B are by far the most abundant with bulk concentrations mostly above 1000 µg/g and 30 µg/g, respectively. All other trace elements showing relative enrichments are generally present in low concentrations (µg/g level), except Sr in carbonate-bearing serpentinites (thousands of µg/g). In situ data indicate that concentrations of Cl, B, Sr, U, Sb, Rb and Cs are, and that of Li can be, increased by serpentinization. These elements are largely hosted in serpentine (lizardite and chrysotile, but not antigorite). Aragonite precipitation leads to significant enrichments in Sr, U and B, whereas calcite is important only as an Sr host. Commonly observed brucite is trace element-poor. The overall enrichment patterns are comparable among serpentinites from mid-ocean ridges, passive margins and fore-arcs, whereas the extents of enrichments are often specific to the geodynamic setting. Variability in relative trace element enrichments within a specific setting (and locality) can be several orders of magnitude. Mid-ocean ridge serpentinites often show pronounced bulk-rock U enrichment in addition to ubiquitous Cl, B and Sr enrichment. They also exhibit positive Eu anomalies on chondrite-normalized rare earth element plots. Passive margin serpentinites tend to have higher overall incompatible trace element contents than mid-ocean ridge and fore-arc serpentinites and show the highest B enrichment among all the studied serpentinites. Fore-arc serpentinites are characterized by low overall trace element contents and show the lowest Cl, but the highest Rb, Cs and Sr enrichments. Based on our data, subducted dehydrating serpentinites are likely to release fluids with high B/Nb, B/Th, U/Th, Sb/Ce and Sr/Nd, rendering them one of the potential sources of some of the characteristic trace element fingerprints of arc magmas (e.g. high B/Nb, high Sr/Nd, high Sb/Ce). However, although serpentinites are a substantial part of global subduction zone chemical cycling, owing to their low overall trace element contents (except for B and Cl) their geochemical imprint on arc magma sources (apart from addition of H2O, B and Cl) can be masked considerably by the trace element signal from subducted crustal components.

Low-temperature experiments of sediment core GeoB6229-6 at the South American continental margin off the Rio de la Plata estuary

With various low-temperature experiments performed on magnetic mineral extracts of marine sedimentary deposits from the Argentine continental slope near the Rio de la Plata estuary, a so far unreported style of partial magnetic self-reversal has been detected. In these sediments the sulphate-methane transition (SMT) zone is situated at depths between 4 and 8 m, where reductive diagenesis severely alters the magnetic mineral assemblage. Throughout the sediment column magnetite and ilmenite are present together with titanomagnetite and titanohematite of varying compositions. In the SMT zone (titano-)magnetite only occurs as inclusions in a siliceous matrix and as intergrowths with lamellar ilmenite and titanium-rich titanohematite, originating from high temperature deuteric oxidation within the volcanic host rocks. These abundant structures were visualized by scanning electron microscopy and analysed by energy dispersive spectroscopy. Warming of field-cooled and zero-field-cooled low-temperature saturation remanence displays magnetic phase transitions of titanium-rich titanohematite below 50 K and the Verwey transition of magnetite. A prominent irreversible decline characterizes zero-field cooling of room temperature saturation remanence. It typically sets out at ~210 K and is most clearly developed in the lower part of the SMT zone, where low-temperature hysteresis measurements identified ~210 K as the blocking temperature range of a titanohematite phase with a Curie temperature of around 240 K. The mechanism responsible for the marked loss of remanence is, therefore, sought in partial magnetic self-reversal by magnetostatic interaction of (titano-)magnetite and titanohematite. When titanohematite becomes ferrimagnetic upon cooling, its spontaneous magnetic moments order antiparallel to the (titano-)magnetite remanence causing an drastic initial decrease of global magnetization. The loss of remanence during subsequent further cooling appears to result from two combined effects (1) magnetic interaction between the two phases by which the (titano-)magnetite domain structure is substantially modified and (2) low-temperature demagnetization of (titano-)magnetite due to decreasing magnetocrystalline anisotropy. The depletion of titanomagnetite and superior preservation of titanohematite is characteristic for strongly reducing sedimentary environments. Typical residuals of magnetic mineral assemblages derived from basaltic volcanics will be intergrowths of titanohematite lamellae with titanomagnetite relics. Low-temperature remanence cycling is, therefore, proposed as a diagnostic method to magnetically characterize such alteration (palaeo-)environments.

Reflection microscopy and geochemistry at DSDP Leg 55 Holes

Magnetic properties of volcanic rocks are controlled mainly by the physical and chemical state of their constituent ferromagnetic minerals. The most important parameters determining magnetic properties are concentration, composition, grain size, and oxidation state. In sea floor basalts, the main ferromagnetic minerals are titanomagnetites which are either unoxidized or, more commonly, have undergone various degrees of posteruptive low-temperature oxidation to become cationdeficient titanomagnetites, or titanomaghemites. The effects of this low-temperature alteration are seen in the increase of Curie temperature and decrease of saturation magnetization and lattice parameter of ferromagnetic minerals (Readman and O'Reilly, 1972). It is now believed that titanomaghemitization of newly formed mid-ocean ridge crust proceeds with a time constant of about 1 m.y., accompanying drastic decrease of the intensity of the natural remanent magnetization (NRM) (Johnson and Atwater, 1977).

Confined crystallization of nanolayered poly(ethylene terephthalate) using X-ray diffraction methods

The development of crystalline lamellae in ultra-thin layers of poly(ethylene terephthalate) PET confined between polycarbonate (PC) layers in an alternating assembly is investigated as a function of layer thickness by means of X-ray diffraction methods. Isothermal crystallization from the glassy state is in-situ followed by means of small-angle X-ray diffraction. It is found that the reduced size of the PET layers influences the lamellar nanostructure and induces a preferential lamellar orientation. Two lamellar populations, flat-on and edge-on, are found to coexist in a wide range of crystallization temperatures (Tc = 117–150 °C) and within layer thicknesses down to 35 nm. Flat-on lamellae appear at a reduced crystallization rate with respect to bulk PET giving rise to crystals of similar dimensions separated by larger amorphous regions. In addition, a narrower distribution of lamellar orientations develops when the layer thickness is reduced or the crystallization temperature is raised. In case of edge-on lamellae, crystallization conditions also influence the development of lamellar orientation; however, the latter is little affected by the reduced size of the layers. Results suggest that flat-on lamellae arise as a consequence of spatial confinement and edge-on lamellae could be generated due to the interactions with the PC interface. En este trabajo se investiga mediante difracción de rayos X a ángulos bajos (SAXS) y a ángulos altos (WAXS), la cristalización de láminas delgadas de Polietilén tereftalato (PET) confinadas entre láminas de Policarbonato (PC), tomando como referencia PET sin confinar. El espesor de las capas de PET varía entre 35nm y 115 nm. Se realizaron medidas de difracción a tres temperaturas de cristalización (117ºC, 132ºC y 150ºC) encontrándose que el reducido espesor de las capas de PET influye en la estructura lamelar que se desarrolla, induciendo una orientación preferente de las láminas. Se integró la intensidad difractada alrededor del máximo en SAXS para obtener una representación de la intensidad en función del ángulo acimutal. Mediante análisis de mínimos cuadrados se separó la curva experimental obtenida en tres contribuciones diferentes: una función Gausiana que describe la distribución de las orientaciones de las lamelas, una función lorenziana asociada a los máximos meridionales (asociados a las interfases PET-PC) y un background constante. Por otra parte la cantidad de material cristalizado se estimó asumiendo que la intensidad del background en el barrido acimutal, una vez restado el background del primer difractograma (sin máximos en SAXS) se asocia con la contribución del material isotrópico que resta en la muestra cristalizada. Se observa la coexistencia de dos poblaciones de lamelas: flat-on y edge-on. A medida que el espesor de las láminas de PET disminuye la población de las lamelas flat-on experimenta los siguientes cambios: 1) la distribución de orientación se estrecha, 2) la fracción de material cristalizado orientado aumenta, 3) la cinética de cristalización se ralentiza y 4) el largo espaciado aumenta es decir las regiones amorfas entre lamelas aumentan su tamaño. Parece demostrarse que es en las primeras etapas del crecimiento lamelar cuando la restricción espacial fuerza a las lamelas a esta orientación tipo flat-on frente a la orientación edge-on.

Pathogenetic sequence for aneurysm revealed in mice underexpressing fibrillin-1

Dissecting aortic aneurysm is the hallmark of Marfan syndrome (MFS) and the result of mutations in fibrillin-1, the major constituent of elastin-associated extracellular microfibrils. It is yet to be established whether dysfunction of fibrillin-1 perturbs the ability of the elastic vessel wall to sustain hemodynamic stress by disrupting microfibrillar assembly, by impairing the homeostasis of established elastic fibers, or by a combination of both mechanisms. The pathogenic sequence responsible for the mechanical collapse of the elastic lamellae in the aortic wall is also unknown. Targeted mutation of the mouse fibrillin-1 gene has recently suggested that deficiency of fibrillin-1 reduces tissue homeostasis rather than elastic fiber formation. Here we describe another gene-targeting mutation, mgR, which shows that underexpression of fibrillin-1 similarly leads to MFS-like manifestations. Histopathological analysis of mgR/mgR specimens implicates medial calcification, the inflammatory–fibroproliferative response, and inflammation-mediated elastolysis in the natural history of dissecting aneurysm. More generally, the phenotypic severity associated with various combinations of normal and mutant fibrillin-1 alleles suggests a threshold phenomenon for the functional collapse of the vessel wall that is based on the level and the integrity of microfibrils.

Glycerol Is a Suberin Monomer. New Experimental Evidence for an Old Hypothesis1

The monomer composition of the esterified part of suberin can be determined using gas chromatography-mass spectroscopy technology and is accordingly believed to be well known. However, evidence was presented recently indicating that the suberin of green cotton (Gossypium hirsutum cv Green Lint) fibers contains substantial amounts of esterified glycerol. This observation is confirmed in the present report by a sodium dodecyl sulfate extraction of membrane lipids and by a developmental study, demonstrating the correlated accumulation of glycerol and established suberin monomers. Corresponding amounts of glycerol also occur in the suberin of the periderm of cotton stems and potato (Solanum tuberosum) tubers. A periderm preparation of wound-healing potato tuber storage parenchyma was further purified by different treatments. As the purification proceeded, the concentration of glycerol increased at about the same rate as that of α,ω-alkanedioic acids, the most diagnostic suberin monomers. Therefore, it is proposed that glycerol is a monomer of suberins in general and can cross-link aliphatic and aromatic suberin domains, corresponding to the electron-translucent and electron-opaque suberin lamellae, respectively. This proposal is consistent with the reported dimensions of the electron-translucent suberin lamellae.

Heterogeneity and Photoinhibition of Photosystem II Studied with Thermoluminescence1

Thermoluminescence (TL) signals were recorded from grana stacks, margins, and stroma lamellae from fractionated, dark-adapted thylakoid membranes of spinach (Spinacia oleracea L.) in the absence and in the presence of 2,6-dichlorphenylindophenol (DCMU). In the absence of DCMU, the TL signal from grana fractions consisted of a homogenous B-band, which originates from recombination of the semi-quinone QB− with the S2 state of the water-splitting complex and reflects active photosystem II (PSII). In the presence of DCMU, the B-band was replaced by the Q-band, which originates from an S2QA− recombination. Margin fractions mainly showed two TL-bands, the B- and C-bands, at approximately 50°C in the absence of DCMU, and Q- and C-bands in the presence of DCMU. The C-band is ascribed to a TyrD+-QA− recombination. In the absence of DCMU, the fractions of stromal lamellae mainly gave rise to a TL emission at 42°C. The intensity of this band was independent of the number of excitation flashes and was shifted to higher temperatures (52°C) after the addition of DCMU. Based on these observations, this band was considered to be a C-band. After photoinhibitory light treatment of uncoupled thylakoid membranes, the TL intensities of the B- and Q-bands decreased, whereas the intensity at 45°C (C-band) slightly increased. It is proposed that the 42 to 52°C band that was observed in marginal and stromal lamellae and in photoinhibited thylakoid membranes reflects inactive PSII centers that are assumed to be equivalent to inactive PSII QB-nonreducing centers.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).