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We investigate the effects of external harmonic forcing on flow through a duct with square cross-section containing two circular orifice plates – a double-orifice cavity – at an operating condition where self-sustained limit cycle oscillations are observed. When the oscillatory flow is periodically forced at a frequency $f_f$ near its natural frequency $f_n$ ($0.9\leqslant f_f /f_n \leqslant 1.1$), it undergoes lock-in and amplitude suppression through synchronous quenching. We observe phase-drifting (or phase-slipping) prior to lock-in that happens via a saddle-node bifurcation. However, when the flow system is forced far from its natural frequency ($0.8\leqslant f_f /f_n\leqslant 0.9$ and $1.1\leqslant f_f /f_n\leqslant 1.4$) lock-in happens via asynchronous quenching through a Neimark–Sacker bifurcation (torus death). In asynchronous quenching, phase-drifting and phase-trapping are observed before lock-in. An asymmetry is present in the synchronization map on forcing either side of the natural frequency, which becomes more pronounced in the asynchronous quenching regime. There is also an observed saturation of the synchronization map for $f_f/f_n\gt 1$ over the range of frequencies explored. Subharmonic synchronization or $1:2$ lock-in with period-two oscillations is also observed when the system is forced near $f_n/2$ ($ 0.49 \leqslant f_f /f_n \leqslant 0.51$). The route to lock-in consists of a three frequency regime where subharmonics of the forcing frequency ($f_f/2$ and $f_f/3$) play an important role in the dynamics. The transition from $1:1$ to $1:2$ lock-in occurs via a de-lock-in regime ($ 0.55 \leqslant f_f /f_n \leqslant 0.65$), where a lock-in boundary is present; i.e. the system delocks after lock-in if the amplitude is raised beyond a critical value. The de-lock-in regime is also characterized by a nonlinear phase drift after de-lock-in and a significant jump in the forcing amplitude for lock-in for $f_f/f_n=0.6$. Amplification is observed for $f_f/f_n\gt 1$ and also in the $1:2$ lock-in and de-lock-in regimes where the total signal power exceeds the unforced system’s power for small increases in forcing amplitude after lock-in. Based on these results, we identify the asynchronous quenching regime for $f_f/f_n\lt 1$ as the optimal frequency range where active control is most effective. Finally, we introduce a reduced-order phenomenological model based on vortex–acoustic interaction dynamics from first principles. The model correctly identifies the four regimes, their dynamics leading to lock-in, and asymmetry and saturation in the synchronization map.
A sustainable pathway for valorizing the growing volume of lignin-rich organic feedstocks (LRFs) in emerging economies is to convert them into biochar to sequester carbon and improve soil fertility. However, biochar derived from such LRF may not always show favorable outcomes during soil application. Their interaction with the soil–plant–microbial ecosystem is very complex, and comparative investigations with other common types of biochars are lacking. This study investigated the impact of walnut shell biochar (WSB) and wood chip biochar (WCB) on soil biological properties and crop yield during the growth of Solanum lycopersicum L., and compared them with those of plant waste biochar (PWB) derived from agricultural plant residues. Among biochar variants, only PWB (1% w/w) has increased tomato yield compared to unamended soil. It also showed better carbon mineralization that stemmed from its higher degradability, lower carbon content, and higher H/C ratio. In contrast, WSB showed a relatively higher hydrophobicity, carbonization, and aromaticity that reduced its accessibility to soil microorganisms. Despite these characteristics and higher ash content, WSB did not lower soil enzyme and microbial activity, unlike WCB. At the same time, WSB did not improve crop yield. Mixing WSB (3% w/w) with soil has slightly enhanced the soil carbon stabilization. The high carbon recalcitrance of LRF may necessitate longer aging in soil compared with PWB to showcase any measurable (short/long) benefits to crop yield and soil characteristics.
Late medieval Italy witnessed the widespread rise of the cult of the Virgin, as reflected in the profusion of paintings, sculptures, and fresco cycles created in her honor during this period. The cathedral of papal Orvieto especially reflects the strong Marian tradition through its fresco and stained-glass window narrative cycles. In this study, Sara James explores its complex narrative programs. She demonstrates how a papal plan for the cathedral to emulate the basilica of S. Maria Maggiore in Rome, together with Dominican and Franciscan texts, determined the choices and arrangement of scenes. The result is a tour de force of Marian devotion, superior artistry, and compelling story-telling. James also shows how the narratives promoted agendas tied to the city's history and principal religious feasts. Not only are these works more interesting, sophisticated, and theologically rich than previously realized, but, as James argues, each represents the acme in their respective media of their generation in central Italy.
In the twelfth through fourteenth centuries, at the height of the cult of the Virgin Mary, a rare and rich conflux of past and present events, both authentic and legendary, catapulted Orvieto into the spotlight as a religious, political, and intellectual center. First heresy and political conflict, then popes, prelates, and the occasional king – including Edward I of England in the 1270s and Charles I of France in 1281 – graced the city’s halls and streets. Ritual and ceremony became a way of life. Concurrently, the illustrious churchmen of Orvieto campaigned for a grand new cathedral, begun in 1290, dedicated to the Assumption of the Virgin Mary to honor the devotion of both the city and the founding pope and adorned with magnificent sculpture, mosaics, alabaster and stained-glass windows, and frescoes.
Both outside and inside the Orvieto Cathedral, artistic decoration attests to the deep reverence the citizens of Orvieto had for the Virgin Mary and confirms that her cult thrived in Orvieto. While most cathedral projects saved the facade decoration for last, at Orvieto, art honoring the Virgin appeared there first, publicly proclaiming reverence to her. By 1330, Lorenzo Maitani crowned the central portal with a life-size marble sculpture of the Virgin and Child seated under a bronze canopy and flanked by angels; a backdrop of Marian mosaics was underway. Interior decoration began in the Cappella Maggiore with the resplendent monumental stained-glass window by Giovanni di Bonino, completed in 1334; Ugolino di Prete Ilario reiterated the Orvietan reverence for the Virgin in a comprehensive narrative fresco program, completed in 1384.
Ugolino’s underlying message of Mary as God’s instrument in the Incarnation resonates most strongly in Ugolino’s third vignette, the Infancy of Jesus, which covers the upper band of the north wall. Here his departure from Sienese compositional conventions is strongest. He completely reimagines each scene and adds a new event. Moreover, Ugolino’s gift for compressing a great deal of narrative into one scene is most apparent in this vignette. Four of the five scenes have a related event happening in the background, and the inscriptions often extend the narrative even further. As Mary’s role shifts from wife to mother, her sense of her mission as guardian to the son of God deepens – as does Joseph’s. Such character development and self-awareness exceed that of most previous narrative cycles.
Orvieto’s citizens had long been consumed by the full humanity of Jesus, Mary, and the doctrine of hypostatic union – that Christ was fully human and fully divine – which the Cathar heretics denied. In fact, one of the main points of the Nicene Creed was to elaborate upon the mystery of Jesus’s Incarnation: “begotten, not made, of one Being with the Father … by the power of the Holy Spirit he became incarnate from the Virgin Mary, and was made man.” Therefore, Ugolino almost obsessively promotes the genuineness of Mary’s human substance, which, in turn promotes the verity of Jesus’s full humanity.
As with her earthy life, Mary’s death and bodily assumption into heaven stand apart as remarkable and confirm her status as human, yet higher than any prophet or saint before or after her, except for Jesus himself (Figure 11.1). Whereas in the vignettes on the lower walls, Mary offers examples of moral and faithful living, in the paintings on the east wall, she becomes the model for dying and the attainment of eternal life. Moreover, the events surrounding her death and afterlife in heaven focus solely on her.
Orvieto, a walled city with Etruscan roots, built almost exclusively of locally mined golden tufa, crowns a steep plateau of 325 m (1,066 ft.) (Figure 1.1). Periods of papal residence boosted the population, the economy, and the intellectual sophistication of the city. At the crest of Orvieto’s fame, Francesco Monaldeschi (r. 1280–95), an ambitious bishop from an influential local family, campaigned for an unparalleled monument to the triumph of the true religion – perhaps also to showcase his newly acquired relic of the corporal cloth from the alleged miraculous Mass at Bolsena, which was translated c. 1294. Contemporary documents suggest some papal financing, including indulgences, and note the Opera del Duomo’s penchant for hiring the finest artists in Italy.
Since the fourth century, the highest places in churches, usually covered with domes or conches, have symbolized the celestial realm. Although the subsequent rebuilding of the apse at Orvieto into a more stable square space thwarted the possibility for a rounded conch, the vault of the Cappella Maggiore serves a corresponding purpose (Figure 13.1). As previously mentioned, whereas in most fourteenth-century mural programs, the groin vaults allude to heaven, at Orvieto, the Marian narrative extends into the vault to depict heaven – a hierarchical arrangement more common to Byzantine programs.
The upper band of the south wall concludes the narrative of the Holy Family. Unfortunately, some paintings show damage, with parts of the intonaco missing. Orvietan documents note repainting in the return from Egypt and the Holy Family at the temple. Conservation reports indicate that the artist(s) who did the repainting, probably Il Pastura (c. 1497–99), respected the original composition, per recorded instruction from the Opera del Duomo. Despite some retouching, conservation reports state that the remaining compositions, including the figure arrangements, architecture, landscape, and balustrade, are original to Ugolino.