Finiteness properties of cubulated groups

We give a generalized and self-contained account of Haglund-Paulin's wallspaces and Sageev's construction of the CAT(0) cube complex dual to a wallspace. We examine criteria on a wallspace leading to finiteness properties of its dual cube complex. Our discussion is aimed at readers wishing to apply these methods to produce actions of groups on cube complexes and understand their nature. We develop the wallspace ideas in a level of generality that facilitates their application. Our main result describes the structure of dual cube complexes arising from relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex codimension-1 subgroups of a group G that is hyperbolic relative to P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved results in Sections 7 and 8. Several theorem numbers have changed from the previous versio

Enhanced nonperturbative effects in jet distributions

We consider the triple differential distribution d\Gamma/(dE_J)(dm_J^2)(d\Omega_J) for two-jet events at center of mass energy M, smeared over the endpoint region m_J^2 << M^2, |2 E_J -M| ~ \Delta, \lqcd << \Delta << M. The leading nonperturbative correction, suppressed by \lqcd/\Delta, is given by the matrix element of a single operator. A similar analysis is performed for three jet events, and the generalization to any number of jets is discussed. At order \lqcd/\Delta, non-perturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two and three jet events.Comment: Significant changes made. The first moment does not vanish--the paper has been modified to reflect this. Relations between different numbers of jets still hol

Shape control and whole-life energy assessment of an 'infinitely stiff' prototype adaptive structure

A previously developed design methodology produces optimum adaptive structures that minimise the whole-life energy which is made of an embodied part in the material and an operational part for structural adaptation. Planar and complex spatial reticular structures designed with this method and simulations showed that the adaptive solution achieves savings as high as 70% in the whole-life energy compared to optimised passive solutions. This paper describes a large-scale prototype adaptive structure built to validate the numerical findings and investigate the practicality of the design method. Experimental results show that (1) shape control can be used to achieve 'infinite stiffness' (i.e. to reduce displacements completely) in real-time without predetermined knowledge regarding position, direction and magnitude (within limits) of the external load; (2) the whole-life energy of the structure is in good agreement with that predicted by numerical simulations. This result confirms the proposed design method is reliable and that adaptive structures can achieve substantive total energy savings compared to passive structures

Infinite stiffness structures via active control

Active control has been used in civil engineering structures for a variety of purposes. Although the potential for using deflection-control adaptation to save material has been investigated by a few other authors, little attention has been given to assessing whether these material savings outweigh the energy consumed through control and actuation. Our paper seeks to address this gap, presenting experimental work on a truss with effective infinite stiffness which builds on earlier theoretical studies. Senatore previously developed a design method that produces an optimum adaptive structure that minimises the total energy spent throughout the whole life of the structure (embodied in the materials + operational for the control) (Senatore, et al., 2013). The method was used to design a range of structures from trusses to space frames, both determinate and indeterminate, and it was shown that it allows energy saving up to 70% compared to state of the art optimisation methods. A large scale prototype structure has now been built to validate the numerical findings and investigate the practicality of the method. This paper discusses recent experimental findings and the making of the prototype. Using the insight acquired after the making and testing of the prototype the authors will discuss potential applications of adaptive structures in selection of different scenarios, ranging from cantilever seating tiers in sports stands to lightweight roofs to slender beams with 80:1 span/depth ratio

Space suit

A pressure suit for high altitude flights, particularly space missions is reported. The suit is designed for astronauts in the Apollo space program and may be worn both inside and outside a space vehicle, as well as on the lunar surface. It comprises an integrated assembly of inner comfort liner, intermediate pressure garment, and outer thermal protective garment with removable helmet, and gloves. The pressure garment comprises an inner convoluted sealing bladder and outer fabric restraint to which are attached a plurality of cable restraint assemblies. It provides versitility in combination with improved sealing and increased mobility for internal pressures suitable for life support in the near vacuum of outer space

A right-handed isotropic medium with a negative refractive index

The sign of the refractive index of any medium is soley determined by the requirement that the propagation of an electromagnetic wave obeys Einstein causality. Our analysis shows that this requirement predicts that the real part of the refractive index may be negative in an isotropic medium even if the electric permittivity and the magnetic permeability are both positive. Such a system may be a route to negative index media at optical frequencies. We also demonstrate that the refractive index may be positive in left-handed media that contain two molecular species where one is in its excited state.Comment: 4.1 pages, 4 figures, submitted to Physical Review Letter

Designing adaptive structures for whole life energy savings

Designing structures with minimal environmental impact is emerging as a seriou concern in the construction sector. Conventional structural design practice involves designing first for strength, followed by secondary checks on deflections and other serviceability limits states. If these limits are exceeded, the con-ventional solution has been to add material to increase stiffness. When the design is governed by unpredicta-ble events such as fluctuating loads, strong wind storms or earthquakes, the structure is effectively overde-signed for most of its working life. This paper presents a methodology to design adaptive structures that minimize the whole life energy consumption. The methodology is illustrated on plane pin-jointed trusses, both determinate and indeterminate. Strategically placing actuators allow the internal flow of forces to be ho-mogenized and displacements to be controlled. The actuators only start working when the loads reach a cer-tain threshold. Below this threshold, the structure resists loads mainly passively thereby limiting significantly the operational energy used. It was found that both indeterminate and determinate topologies bring substantial energy savings up to 70% of the total energy

Criteria for the experimental observation of multi-dimensional optical solitons in saturable media

Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons (spatial or spatiotemporal), for their three-dimensional spatiotemporal counterparts such a window \emph{does not} exist, due to the nonlinear loss in glasses.Comment: 8 pages, to appear in Phys. Rev.

Opioids depress cortical centers responsible for the volitional control of respiration

Respiratory depression limits provision of safe opioid analgesia and is the main cause of death in drug addicts. Although opioids are known to inhibit brainstem respiratory activity, their effects on cortical areas that mediate respiration are less well understood. Here, functional magnetic resonance imaging was used to examine how brainstem and cortical activity related to a short breath hold is modulated by the opioid remifentanil. We hypothesized that remifentanil would differentially depress brain areas that mediate sensory-affective components of respiration over those that mediate volitional motor control. Quantitative measures of cerebral blood flow were used to control for hypercapnia-induced changes in blood oxygen level-dependent (BOLD) signal. Awareness of respiration, reflected by an urge-to-breathe score, was profoundly reduced with remifentanil. Urge to breathe was associated with activity in the bilateral insula, frontal operculum, and secondary somatosensory cortex. Localized remifentanil-induced decreases in breath hold-related activity were observed in the left anterior insula and operculum. We also observed remifentanil-induced decreases in the BOLD response to breath holding in the left dorsolateral prefrontal cortex, anterior cingulate, the cerebellum, and periaqueductal gray, brain areas that mediate task performance. Activity in areas mediating motor control (putamen, motor cortex) and sensory-motor integration (supramarginal gyrus) were unaffected by remifentanil. Breath hold-related activity was observed in the medulla. These findings highlight the importance of higher cortical centers in providing contextual awareness of respiration that leads to appropriate modulation of respiratory control. Opioids have profound effects on the cortical centers that control breathing, which potentiates their actions in the brainstem