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  • 1
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    Unknown
    London : Periodicals Archive Online (PAO)
    Journal of historical geography. 1:3 (1975:July) 283 
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 124 (1989), S. 337-364 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Square integrable Wiener functionals may be represented as sums of multiple Itô integrals. This leads to an identification of such functionals with square integrable functions on the symmetric measure space of the Lebesgue spaceR +. When the pointwise product of Wiener functionals is thus carried over, the product takes a pleasing form (cf. Wick's theorem) and various non-commutative perturbations of this “Wiener product” have been considered. Here we employ cohomological arguments to analyse deformations of an abstract Wiener product. This leads to the construction of Lévy fields which are neither bosonic nor fermionic, and also gives rise to homotopies between quasi-free boson and fermion fields. Finally we unify existence and uniqueness results for quantum stochastic differential equations by treating mixed noise differential equations.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 71 (1986), S. 307-320 
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We show that strictly quasi-free Fermion martingales may be expressed as a sum of quantum stochastic integrals with respect to the Fermi creation and annihilation processes and a multiple of the identity.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 2021-06-25
    Description: Uncertainties in modelling volcanic hazards are often amplified in geographically large systems and in volcanoes which have a diverse eruption history that comprises variable eruption compositions and styles from different vent locations. The large ~ 700 km2 Okataina Volcanic Centre (OVC) is a large silicic caldera complex in a geodynamic region of New Zealand which has displayed a range of eruption styles and compositions over its current phase of activity (26 ka - present), including one basaltic maar-forming eruption, one basaltic Plinian eruption, and nine rhyolitic Plinian eruptions. All three of these eruption styles have occurred within the past 3.5 ky, and any of these styles could occur in the event of a future eruption. The location of a future eruption is also unknown. Future vents could potentially open in one of three different possible areas of the OVC: the Tarawera linear vent zone (LVZ) (5 eruptions over the past 26 ky), the Haroharo LVZ (5 eruptions over the past 26 ky), or outside of these LVZs (1 eruption over the past 26 ky). A future rhyolitic or basaltic Plinian eruption from the OVC is likely to generate widespread tephra fall in loads that will cause significant disruption and socio- economic impacts throughout the surrounding region. Past OVC tephra studies have focused on evaluating hazard from a rhyolitic Plinian eruption at select vent locations in the OVC's Tarawera LVZ. Here, we expand upon these past studies by evaluating tephra hazard for all possible OVC eruption vent areas and for both rhyolitic and basaltic Plinian eruption styles, and exploring how these parameters influence tephra hazard forecasts. Probabilistic volcanic hazard model BET_VH and advection-diffusion tephra hazard model TEPHRA2 were used to assess the hazard of accumulating ≥ 10 kg m-2 of tephra from both basaltic Plinian and rhyolitic Plinian eruption styles, occurring from within the Tarawera LVZ, the Haroharo LVZ, and other potential vent areas within the caldera. We present the results of these analyses as a first-order tephra hazard assessment for the entire OVC. Our results highlight the importance of considering all the potential vent locations of a volcanic system, in order to capture the full eruption catalogue in analyses (e.g., 11 eruptions over 26 ky for the OVC, versus only 5 eruptions over 26 ky for the Tarawera LVZ), as well as the full potential distribution of tephra hazard. Although the Tarawera LVZ has been prominently discussed in studies of OVC hazard because of is recent activity (1886 and ~1315 AD), we find that, in the event of future eruption, the likelihood of a vent opening within the Haroharo LVZ (last eruption 5.6 ka) is equivalent (〈 1% difference) to that for the Tarawera LVZ (31.8% compared to 32.5%). We also find that an eruption from within the Haroharo LVZ presents a relatively higher hazard to several localities, such as the town of Kawerau, where the average absolute probability of accumulating ≥ 10 kg m-2 of tephra is 1.3 times greater than for an eruption from within the Tarawera LVZ. While the absolute probabilities of accumulating ≥ 10 kg m-2 of tephra in the next one year from a basaltic Plinian eruption are on average 7.2 times lower than for a rhyolitic Plinian eruption throughout the surrounding region, our results suggest that the hazard posed by a basaltic Plinian eruption does contribute to the overall OVC tephra hazard, raising absolute probabilities for the entire OVC by an order of 0.14, which may have implications when considering sensitive decision-making thresholds.
    Description: Published
    Description: 38
    Description: 3V. Dinamiche e scenari eruttivi
    Description: JCR Journal
    Description: restricted
    Keywords: PVHA ; Okataina Volcanic Centre ; BET_VH ; TEPHRA2 ; volcanic hazard ; 04. Solid Earth::04.08. Volcanology::04.08.08. Volcanic risk
    Repository Name: Istituto Nazionale di Geofisica e Vulcanologia (INGV)
    Type: article
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  • 5
    Publication Date: 1986-01-01
    Print ISSN: 0178-8051
    Electronic ISSN: 1432-2064
    Topics: Mathematics
    Published by Springer
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  • 6
    Publication Date: 2013-09-16
    Description: High-resolution sampling in monogenetic fields has the potential to reveal fine-scale heterogeneity of the mantle, a feature that may be overwhelmed by larger fluxes of magma, or missed by under-sampling. The Quaternary Auckland Volcanic Field (AVF) in northern New Zealand is a basaltic field of 51 small-volume volcanic centres, and is one of the best-sampled examples of a monogenetic volcanic field. We present data for 12 centres in the volcanic field. These show the large compositional variations between volcanoes as well as through single eruptive sequences. Whole-rock compositions range from subalkaline basalt in the larger centres, through alkali basalt to nephelinite in the smallest centres. Fractional crystallization has had a limited effect in many of the centres, but high-pressure clinopyroxene crystallization may have occurred in others. Three end-members are observed in Pb isotope space, indicating that distinct mantle source components are involved in the petrogenesis of the magmas. Whole-rock multi-element patterns show that the larger centres have prominent positive Sr anomalies and lack K anomalies, whereas the smaller centres have prominent negative K anomalies and lack Sr anomalies. The melting parameters and compositions of the sources involved are modelled using trace element ratios and multi-element patterns, and three components are characterized: (1) fertile peridotite with a Pb-isotope composition similar to Pacific mid-ocean ridge basalt; (2) eclogite domains with a HIMU-like isotope composition dispersed within the fertile peridotite; (3) slightly depleted subduction-metasomatized peridotitic lithospheric mantle (containing c . 3% subduction fluids). Modelling shows that melting in the AVF begins in garnet-bearing fertile asthenosphere (with preferential melting of eclogite domains) and that melts are variably diluted by melts of the lithospheric source. The U–Th isotope compositions of the end-members in the AVF show 230 Th excess [( 230 Th/ 232 Th) ratios of 1·11–1·38], with the samples of lower ( 230 Th/ 232 Th) exhibiting higher ( 238 U/ 232 Th), which we attribute to the dilution effect of the melts from the lithospheric mantle source. Modelling reveals a correlation between melting in the asthenosphere, the degree of melting and incorporation of the metasomatized lithospheric mantle source, and the resultant size of the volcanic centre. This suggests that the scale of the eruption may essentially be controlled by asthenospheric mantle dynamics.
    Print ISSN: 0022-3530
    Electronic ISSN: 1460-2415
    Topics: Geosciences
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  • 7
    Publication Date: 2015-10-20
    Print ISSN: 0091-7613
    Electronic ISSN: 1943-2682
    Topics: Geosciences
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  • 8
    Publication Date: 2015-05-20
    Description: Assessing the impact of crustal assimilation on the composition of oceanic arc lavas is important if source composition is to be correctly interpreted. This is particularly the case in the Lesser Antilles where lavas encompass a very large range in radiogenic isotope compositions. Here we present new 176 Hf/ 177 Hf and trace element data for a suite of samples from St Lucia in the southern Lesser Antilles arc where assimilation of sediments located within the arc crust has been shown to influence significantly Sr–Nd–Pb isotope compositions. We show that a high rate of assimilation (r = 0·8) of sediment is responsible for the co-variation of Th/Th*, La/Sm, 87 Sr/ 86 Sr, 206/207/208 Pb/ 204 Pb, 143 Nd/ 144 Nd and 176 Hf/ 177 Hf towards extreme ‘continental’ compositions. Lavas that escaped sediment assimilation have a typical oceanic arc signature and provide the best indication of mantle source characteristics beneath St Lucia. They display similar Ba/Th, La/Sm and Nd isotopic compositions to lavas further north in the arc, but with slightly more radiogenic Sr and Pb. Addition of less than 2% of local bulk subducting sediment, or less than 3·5% of sediment partial melt or fluid, to the mantle wedge can explain these compositions; these estimates are similar to those previously proposed for the northern arc. After correction for the effects of sediment assimilation, the St Lucia lavas have only slightly more radiogenic Pb and Sr isotope signatures compared with the northern islands; this can be attributed to differences in the isotopic composition of the local subducting sediment rather than to greater sediment input, as has been previously proposed. Comparison of St Lucia with the other southern Lesser Antilles islands suggests that similar mantle source compositions exist beneath Martinique, St Vincent and perhaps Bequia, whereas a more ‘continental’ source might characterize Ile de Caille, Kick ’em Jenny and Grenada.
    Print ISSN: 0022-3530
    Electronic ISSN: 1460-2415
    Topics: Geosciences
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  • 9
    Publication Date: 2015-05-23
    Description: Eruptions of basaltic material in small-scale volcanic fields located in intraplate settings display a very diverse range in physical and chemical characteristics. Despite its relevance to the understanding of volcanic hazards, the relationship between physical properties of eruptions (explosivity, volume, location) and chemical composition of erupted products has, to date, not been investigated. Here we present a relationship between mantle heterogeneity and extents of partial melting, and both erupted volumes and eruptive style from the Auckland Volcanic Field (New Zealand), and we suggest that this provides a general model for small-scale "monogenetic" magmatic systems globally. Small volcanic centers consistently take the form of nephelinitic tuff rings and scoria cones, whereas larger centers are produced from effusive eruptions of less alkalic magmas. Nephelinitic melts are generated by melting of a deep, carbonated source, whereas less alkalic melts are the products of melting of a shallower, noncarbonated source. U-Th-Ra isotope data from eruptions closely paired in space and time show that mixing between magmas is extremely limited as a consequence of different ascent mechanisms due to differential segregation of melts from varying sources (early, carbonated melts ascending by higher porosity channels, and later, uncarbonated melts by a more diffusive regime). This suggests that extraction of melt is nearly instantaneous in these environments. Our results stress the importance of melting and magma dynamics in determining the size and style of eruptions in small volcanic fields, and suggest that mantle controls should be an important consideration in volcanic hazard assessment.
    Print ISSN: 0091-7613
    Electronic ISSN: 1943-2682
    Topics: Geosciences
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  • 10
    Publication Date: 2014-02-08
    Description: We develop fully noncommutative Feynman–Kac formulae by employing quantum stochastic processes. To this end, we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterized under alternative assumptions of separability or Markov regularity. Our results generalize those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.
    Print ISSN: 0024-6107
    Electronic ISSN: 1469-7750
    Topics: Mathematics
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