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We view our denition of factorization algebra as a dierential geometric ana log of a denition introduced by Beilinson and Drinfeld blood pressure medication enalapril side effects order line sotalol. However heart attack grill death buy 40mg sotalol visa, the denition we use is very closely related to other denitions in the literature blood pressure 140 over 90 order sotalol discount, in particular to the Segal axioms prehypertension in pregnancy discount 40mg sotalol with mastercard. This structure is the analog fetal arrhythmia 30 weeks buy 40 mg sotalol visa, in the world of eld theory blood pressure 210120 order sotalol 40 mg with amex, of the Poisson bracket on the commutative algebra of observables. This states that, pro vided certain obstruction groups vanish, the classical factorization al gebra associated to a classical eld theory admits a quantization. Fur ther, the set of quantizations is parametrized, order by order in ~, by the space of deformations of the Lagrangian describing the classical theory. We claim that this theorem is a mathematical encoding of the perturbative methods developed by physicists. This quantization theorem applies to many examples of physical interest, in cluding pure Yang-Mills theory and models. For pure Yang-Mills theory, it is shown in Costello (2011b) that the relevant obstruction groups vanish and that the deformation group is one-dimensional; thus there exists a one-parameter family of quantizations. In Li and Li (2016), the topological B-model with target a complex manifold X is constructed; the obstruction to quantization is that X be Calabi-Yau. Li and Li show that the observables and correlations functions recovered by their quantization agree with well-known formulas. Other examples are considered in Gwilliam and Grady (2014), Costello (2010, 2011a), and Costello and Li (2011). We will explain how (under certain additional hypotheses) the factorization algebra associated to a perturbative quantum eld theory encodes the correlation functions of the theory. This fact justies the assertion that factorization algebras encode a large part of quantum eld theory. We also show in this volume how factorization algebras provide a convenient unifying language for many concepts in topological and quantum eld theory. Volume 2, which is more technical, derives the link be tween the concept of perturbative quantum eld theory as developed in Costello (2011b) and the theory of factorization algebras. The motivating example of quantum mechanics the model problems of classical and quantum mechanics involve a particle moving in some Euclidean space Rn under the inuence of some xed eld. As a narrative strategy, we describe a kind of cartoon of a physical experiment, and we ask that physicists accept this cartoon as a friendly caricature elucidating the features of physics we most want to emphasize. For the general framework we want to present, the details of the physical system under study are not so important. However, for con creteness, we will focus attention on a very simple system: that of a single particle conned to some region of space. We conne our particle inside some box and occasionally take measurements of this system. The set of possible trajectories of the particle around the box constitute all the imaginable behaviors of this particle; we might describe this space of behaviors mathematically as Maps(I, Box), where 1. We say the set of possible behaviors forms a space of elds on the timeline of the particle. The behavior of our theory is governed by an action functional, which is a function on Maps(I, Box). The simplest case typically studied is the massless free eld theory, whose value on a trajectory f: I > Box is Z S (f) = (f (t), f(t))dt. Let us start by considering the simpler case where our particle is treated as a classical system. In that case, the trajectory of the particle is constrained to be in a solution to the Euler-Lagrange equations of our theory, which is a dierential equation determined by the action functional. For example, if the action functional governing our theory is that of the massless free theory, then a map f: I > Box satises the Euler-Lagrange equation if it is a straight line. Since the trajectory of our particle is constrained to be a solution to the Euler-Lagrange equa tion, the only measurements one can make are functions on the space of solutions to the Euler-Lagrange equation. If U R is an open subset, we will let Fields(U) denote the space of elds on U, that is, the space of maps f: U > Box. We will cl think of Obs (U) as the collection of observables for our classical system that only depend upon the behavior of the particle during the time period U. As U varies, the cl algebras Obs (U) vary and together constitute a cosheaf of commutative algebras on R. The notion of measurement is fraught in quantum theory, but we will take a very concrete view. The measurement is then how our measurement device has changed due to the interaction. Instead of considering all possible observables, we might also consider those observables which occur within a specied time period. For every open subset U R, we have a set Obs(U) of observables one can make during U. We think of Obs(U) as being the collection of ways of coupling a measure ment device to our system during the time period U. Measurements (and so observables) dier qual itatively in the classical and quantum settings. If we study a classical particle, the system is not noticeably disturbed by measurements, and so we can do multiple measurements at the same time. We also have maps Obs(I) Obs(J) > Obs(K) for every pair of disjoint intervals I, J contained in an interval K, as well as the maps that let us combine observables on disjoint intervals. For a quantum particle, however, a measurement typically disturbs the system signicantly. Taking two measurements simultaneously is incoherent, as the mea surement devices are coupled to each other and thus also aect each other, so that we are no longer measuring just the particle. Quantum observables thus do not form a cosheaf of commutative algebras on the interval. However, there are no such problems with combining measurements occurring at dierent times. If U, U0 are disjoint open subsets of R, and U, U0 V where V is also open, then there is a map 0 O0 is dened by coupling our system to measuring device O during the period U and to device O0 during the period U0. Further, there are maps for an nite collection of dis joint time intervals contained in a long time interval, and these maps are compatible under composition of such maps. In the bulk of this two-volume book, we will be considering perturbative quantum theory. In perturbative theory, therefore, the space Obs(U) of observables on an open subset U is a C[[~]]-module, and the product maps are C[[~]]-linear. The correspondence principle states that the quantum theory, in the ~ > 0 limit, must reproduce the classical theory. The vector space Obs (U) of quantum ob servables is a at C[[~]]-module such that modulo ~, it is cl equal to the space Obs (U) of classical observables. They say, roughly, that the observables of a quantum eld theory form a factor ization algebra, which is a quantization of the factorization algebra associated to a classical eld theory. The main theorem presented in this two-volume book is that one can use the techniques of perturbative renormalization to construct factor ization algebras perturbatively quantizing a certain class of classical eld theories (including many classical eld theories of physical and mathematical interest). As we have mentioned, this rst volume focuses on the general theory of factorization algebras and on simple examples of eld theories; this result is derived in volume 2. The principles we have described so far indicate that the observables of a quantum mechanical system should assign, to every open subset U R, a vector space Obs(U), together with a product map 0 Obs(U) Obs(U) > Obs(V) if U, U0 are disjoint open subsets of an open subset V. It turns out that in the case of quantum mechanics, the factorization algebra produced by our quantization procedure has a special property: it is locally con stant (see Section 4). This means that the map Obs((a, b)) > Obs(R) is an isomor phism for any interval (a, b). Let A be denote the vector space Obs(R); note that A is canonically isomorphic to Obs((a, b)) for any interval (a, b). The product map Obs((a, b)) Obs((c, d)) > Obs((a, d)) when a < b < c < d, becomes, via this isomorphism, a product map m: A A > A. The axioms of a factorization algebra imply that this multiplication turns A into an associative algebra. This kind of geometric interpretation of algebra should be familiar to topolo gists: associative algebras are algebras over the operad of little intervals in R, and this is precisely what we have described. As we explain in Section 4, this relation ship continues and so our quantization theorem produces many new examples of algebras over the operad En of little n-discs. An important point to take away from this discussion is that associative al gebras appear in quantum mechanics because associative algebras are connected with the geometry of R. As we will see later, when one considers topological quantum eld theories on n-dimensional space times, one nds a structure reminiscent of an En-algebra instead of an E1-algebra. Remark: As a caveat to the strong assertion above (and jumping ahead of our story), note that for a manifold of the form X > R, one can push forward a factorization algebra Obs on X R to a factorization algebra Obs on R along the projection map: X R > R. Hence, a quan tization of a higher dimensional theory will produce, via such pushforwards to R, deformations of associative algebras, but knowing only the pushforward is typi cally insucient to reconstruct the factorization algebra on the higher dimensional manifold. A preliminary denition of prefactorization algebras Below (see Section 1) we give a more formal denition, but here we provide the basic idea. The simplest case of this compatibility is that if U V W is a sequence of open sets, the map F (U) > F (W) agrees with the composition through F (V)). Remark: A prefactorization algebra resembles a precosheaf, except that we tensor the cochain complexes rather than taking their direct sum. In fact, they satisfy a kind of local-to-global principle in the sense that the observables on a large open set are 3. The notion of a factorization algebra (Section 1) makes this local-to-global condition precise. Prefactorization algebras in quantum eld theory the (pre)factorization algebras of interest in this book arise from perturbative quantum eld theories. We have already discussed in Section 1 how factorization algebras appear in quantum mechanics. In this section we will see how this picture extends in a natural way to quantum eld theory. The manifold M on which the prefactorization algebra is dened is the space time manifold of the quantum eld theory. If U M is an open subset, we will in terpret F (U) as the collection of observables (or measurements) that we can make which only depend on the behavior of the elds on U. Performing a measurement involves coupling a measuring device to the quantum system in the region U. In that situation, one can imagine the space-time M as being of the form M = A (0, t), where A is the interior of the accelerator and t is the duration of our experiment. In this situation, performing a measurement on an open subset U M is some thing concrete. Let us take U = V (, ), where V A is some small region in the accelerator and where (, ) is a short time interval. Performing a measurement on U amounts to coupling a measuring device to our accelerator in the region V, starting at time and ending at time. For example, we could imagine that there is some piece of equipment in the region V of the accelerator, which is switched on at time and switched o at time. Then we can turn O1 and O2 on at any times we like, including for overlapping time intervals. However, we could imagine inserting O1 into region V1 during the time interval (a, b); and then removing O1, and inserting O2 into the overlapping region V2 for the disjoint time interval (c, d). These simple considerations immediately suggest that the possible measure ments we can make of our physical system form a prefactorization algebra. Then, by combining measurements in the way outlined above, we would expect to have maps 0 Obs(U) Obs(U) > Obs(V) whenever U, U0 are disjoint open subsets of an open subset V. The associativity and commutativity properties of a prefactorization algebra are evident. In the approach to quantum eld theory considered in this book, the factorization algebra of observables will be a factorization algebra of cochain complexes. We will repeatedly mention observables in a gauge theory, since these kinds of cohomological aspects are well-known for such theores. If O Obs (U) is an observable of cohomological degree 0, then the equation dO = 0 can often be interpreted as saying that O is compatible with the gauge symmetries of the 0 theory. Thus, only those observables O Obs (U) that are closed are physically meaningful. Often, two observables on U are physically indistinguishable (that is, they can not be distinguished by any measurement one can perform). In the example of an accelerator outlined above, two measuring devices are equivalent if they always produce the same expectation values, no matter how we prepare our system, or no matter what boundary conditions we impose.

A handful of texts from Israel continued to be read blood pressure chart symptoms order 40 mg sotalol with mastercard, copied pulse pressure 43 buy cheap sotalol 40 mg, and embellished by scribes from the conquered kingdom of Israel pulse pressure 62 discount sotalol online visa. Wright Assyria incorporated the conquered kingdom of Israel into its system of prov inces blood pressure 0f 165 cheap sotalol 40mg with mastercard. Sennacherib and his Assyrian armies lifted their siege of Jerusalem and left the kingdom of Judah intact heart attack cough purchase 40 mg sotalol. Boosting the impact of these social changes was the devastation that the Assyrian armies wrought on the Judahite countryside blood pressure medication kidney cancer purchase generic sotalol canada, effectively reducing the kingdom to a city-state of Jerusalem and its environs. Later the king of Damascus formed a coalition with Israel, Gaza, Ashkelon, and the Arabs. When the coalition attempted to force Judah to join, Judah called on Tiglath-pileser for help, paying a high fee for protection. When Sargon unpredictably fell on the battlefield, the empire was riveted by major revolts in Babylonia and the Levant. The king of Babylon appears to have coordinated his resistance with Hezekiah in Judah. Against both, Sennacherib marched with formidable force, punishing both and establishing Assyrian hegem ony for decades to come. Introduction 3 the Assyrian conquests were accompanied by the promotion of foreign trade. In her chapter, Sandra Blakely discusses this development from the perspective of Greece and the Aegean world. Sennacherib had opened the door to Aegean entrepreneurs, and they continued to benefit directly from Assyrian hegemony. From this point, we witness increased mercantile and mercenary Greek presence in the East. In Judah (and elsewhere), cultural goods of exchange were not only confined by and large to the elite, but they also appear dispropor tionately in ritual and feasting contexts, which are rich in symbolic communication. As Blakely points out, the seventh century witnessed an explo sion of exchange between East and West, but this heyday would not have been possible without the late eighth century developments. The focus of this volume is on Judah, and the chapters of part 1 set the scene by profiling the states that neighbored Judah. It was home to several well-planned cities with fortifications, monumental public buildings, walls, water supply sys tems, and residential buildings. Some of the remarkable cities include its capital Samaria, the administrative center Shechem, and the impressive trade city of Me giddo. Besides urban areas, the kingdom had rural settlements, which bolstered the economy through the production of olive oil. As a stratified society, the tradi tional kinship-based social structures prevailed in the rural sector, while the nuclear family systems became the norm in urban centers. The cities also appear to have been much more ethnically heterogeneous than the rural sites. During the 730s and 720s, Assyrian campaigns systematically destroyed al most every city, village, and farm in the kingdom. Its purpose was to prevent revolts, increase the size of the army, and pro vide labor for construction projects (such as cities) and agricultural work. These prov inces became the site of resettlement for deportees from other regions. Bethsaida began as an impressively planned capital for the kingdom of Ge shur, and it ended in a dramatic conflagration at the hands of Assyrian soldiers. It is one of the best-preserved capital cities from the Iron Age, and as such, it offers a rare glimpse of urban life in the Levant during the eighth century. The terraced layout of the mound (unique to this site) witnesses to expert city-planning; most towns emerged as natural outgrowths from earlier, smaller settlements. If Arav is right to draw comparisons to the Roman Empire, the width of the road (suitable for carts and wagons) suggests that the region was pacified and enjoyed the rule of law in the years before its destruction. It illustrates, perhaps better than any other site in the Levant, how gates served as the center of political and religious life in Iron Age cities. Royal granaries, cultic paraphernalia, and seats for city elders have all been uncovered at there. Philistia is an important region lying west of Judah along the southern Med iterranean coast. Gitin surveys the finds related to a wide array of vessel types (bowls, scoops, chalices, kraters, cooking pots, jar-kraters, storage jars, hole mouth jars, amphora, jugs, and juggles). The developments there contrast with what we witness in Judah, where the Assyrians destroyed most of the major cities and did little if anything to promote its economic recovery. Bruce Routledge turns our attention across the Jordan, to the three kingdoms (Ammon, Moab, and Edom) that neighbored Judah to the east. Most towns were fortified with walls and gateways with houses laid out along the arc of the town wall. In other areas, clusters of buildings are organized around shared courtyards and irregular alleys. Textiles (with complex patterns) were produced for exchange as part of a cottage industry. Ritual activities included visits and pilgrimages to isolated cultic sites, setting up figurines and/or symbolic stones, sprinkling and Introduction 5 purification, the use of aromatics, and the presentation of offerings in miniature vessels. When the Assyrians appeared on the horizon, Judah and neighboring states in the Levant were forced to serve as a buffer to Egypt, now ruled by Libyan kings who were reluctant to assimilate to Egyptian ways. In the Hebrew Bible, we hear often of delegations from Judah pleading for Egyptian assistance. While those calls for help went mostly unheeded, Egypt still made itself felt in the southern Levant. That impact turns out to be more mercantile than military: As Egypt could no long meet its own commercial demands, it came to depend more heavily on trade abroad. The eighth century was characterized by lethargy and disinterest in for eign involvement, and by the end of the century, the Delta and Middle Egypt had become a virtual political vacuum. The vacuum was eventually filled by the sud den rise of a new regime: Kush (Nubia). This new cast of rulers set their sights on the old imperial terrain of the New Kingdom. In the early seventh century, Egypt continued to meddle abroad until Assyria (under Esarhad don) finally invaded the country and installed puppet kings and governors. While many flocked to urban centers, others moved to repopulate a countryside that had largely been abandoned after the Iron Age I. Yuval Gadot and Efrat Bocher discuss the different styles of buildings in eighth-century Jerusalem and Judah, helping us understand what they tell us about 6 Jacob L. Their contribution treats the Open-Courtyard Building, a two-winged house with an uncovered enclosure in between. By focus ing on this edifice, Gadot and Bocher can demonstrate how the beginning of its use in and around Jerusalem coincides with increasing Assyrian control in the region. The floor plan differs from earlier building types, like the Four-Room House, which have more enclosed, private courtyards. The Open-Courtyard Buildings were likely administrative centers, with their accessible courtyards as public spaces. Examining the various forms in which these edifices were built opens a win dow into eighth-century social and familial patterns. The appearance of the Open-Courtyard Building in Jerusalem sheds light on the extent of Assyrian power and influence over the city, even if the Assyrians never fully conquered it. Tell el-Hesi is a site from the region of Judah where three topographical re gions of Judah come together: the sand dunes and loessal lowlands of the coastal plain, the rolling limestone hills of the Shephelah, and the arid environs of the Negev Desert. Hardin, who surveyed this site and have excavated another one nearby (Khirbet Summeily), demonstrate what we can learn from the Hesi region for the eighth century when we view it against the backdrop of 3,000 years of its history. While Hesi, on the border between Judah and Philistia, has long been consid ered farmland, Blakely and Hardin note that no farmsteads or other signs of farming life have been found in the area. They then proceed to show how the site was likely a center of shepherding and pastoral lifestyle during the ninth and eighth centuries. In examining the available archaeological data in particular, the two ar cheologists note that while charred seeds have been discovered in the region, they are not present at all sites, and no farming implements have been recovered de spite sifting through all excavated soil. Rather than farming towns and villages, many sites in the area such as Tell el-Hesi appear to have been built as forts to Introduction 7 secure the border against Philistia. The shifting of archaeological focus from moments in (biblical) history to the daily lives of common people has been pivotal. Ebeling then introduces a new way of integrating the ar cheological study of ancient Near Eastern life with the ethnographic study of modern inhabitants of this region. While ceramic pottery has been the focus of much attention (due to its diag nostic character that helps us date occupation layers), other objects of daily life are only beginning to receive the attention they deserve. The increasing academic importance of the domestic sphere has also allowed more opportunities to exam ine the role of women in ancient society. As a case study, Ebeling uses a house excavated at Tel Halif (where Oded Borowski has led excavations for many years). Working through room-by-room reconstructions of a house excavated at the site demonstrates how different archaeological disciplines come together to offer a broad picture of ancient domestic life. Cynthia Shafer-Elliott guides us through yet other aspects of everyday life in her chapter on food, cooking, and feasting in eighth-century Judah. Drawing from textual and archaeological evidence, Shafer-Elliott presents a picture of food prac tices that encompasses diet, food preparation, baking, cooking, and feasting. In the late eighth century, the Judahite economy was stretched thin from pay ing annual tribute to the Assyrians. As the burden was felt across all sectors of society, meat became a rarity in the diets of common people (aside from feast times). Most people spent time in production work, either in food preparation or in industries requiring animals that could oth erwise have been slaughtered for their meat.

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After specifying the interface planarity on Instrument side heart attack kid order sotalol, the Al base plate was designed as a milled structure with stiffening ribs blood pressure medication that does not lower heart rate buy sotalol once a day, closed by a thin Al cover plate attached to its bottom by means of screws and dowel pins in order to achieve a box-type structure providing good bending but also adequate torsion stiffness at low sensitivity against thermal gradients heart attack american order sotalol with amex. Figure 5 shows the arrangement of the Scan Drive Unit and Antenna Reflectors on the Base Plate blood pressure chart vaughns 40 mg sotalol mastercard. Drive Unit the Drive Unit is built up with a titanium Housing and a steel Shaft interfacing the two Antenna Reflectors heart attack symptoms in women over 40 order cheap sotalol. The material combination was chosen to optimize for minimum mass and good thermal match at temperature extremes heart attack quotes buy cheap sotalol 40mg line. The Optical Encoder for motor commutation and position feedback is mounted to one side of the Drive Unit Housing. Bearing material is stainless steel 440 C equipped with phenolic resin cages, lubricated with Fomblin Z 25. The motor has independent stators so to provide redundancy and to allow adjustment of the two stators in rotational direction with respect to each other. This feature was included in order to further optimize the system in view of the high required velocity constancy. By rotational adjustment of the redundant stator with respect to the main stator, an additional minimization of the overall detent torque could be realized. Motor commutation and position feedback to the controller is provided by an optical 17-bit encoder in redundant configuration. Alignment cube Scanning shaft Scanning shaft Drive Unit interface provides Housing Reflector alignment provision Encoder Drive Unit interface to Base Blate Figure 7. This value was exceeded by splitting the manufacturing process into several individual sub tasks at different specialized suppliers. The coordination of the related tasks was followed and closely supported in order to minimize the technical and subsequent programmatic risks. It has linear power stages for extremely accurate, wide-bandwidth and high precision tracking control. The power stages are linear (non-switching) and are designed to operate at 27V and at a peak current of up to 2A. These power stages possess two current sensors in the output phases to support full sine-wave commutation, which ensures optimum torque and velocity control characteristics. The use of linear power control and precise control of the operational current guarantees an excellent performance at low drift, high bandwidth and high linearity. In addition there are two enable and status signals for each of the redundant power stages and encoder feedback channels. Specific Development and Test Issues Mass and Inertia Minimization of Welded Baffle In order to achieve the required scan performance (minimum time between the operational points which are earth scan, cold and hot calibration), the system had to be designed for maximum acceleration capability. Since the available torque is limited by the available motor power, the moment of inertia of the rotating part of the mechanism had to be minimized. The thermal baffles (two of them) provide significant contribution to the overall moment of inertia and its mass and radius had therefore to be minimized. Consequently the baffle was designed as a very thin walled structural cylinder (1-mm wall thickness) manufactured out of a bent aluminium plate and stiffened up by means of a radial ring at its one end (close to the Front Ends). The other end of the baffle was attached via screws to a circular plate attached between Drive Unit and Antenna Reflectors (see Figure 8). During vibration testing, a failure of the electron weld seam was identified, so that a re-design of the thermal baffle was necessary. In order to solve the issue, it was decided to manufacture the Baffle structure in a sophisticated manufacturing process from one piece of aluminium so to avoid any welding seams and the critical welding process (Figure 9). The subsequently repeated vibration test was successfully passed without any problem. Thermal Baffles Manufactured as Monolithic Structure (Originally Welded) Minimization of Motor Detent Torque According to the requirement, a maximum scan speed error of 1% shall realized. However, due to the fact that the motor detent torque plays also an important role in achieving good velocity stability, additional measures to reduce the detent torque were identified. It was found that by rotation of one of the two stators by half a stator slot pitch (corresponding to 2. This design feature was consequently included into the design to further optimize for minimum velocity disturbances. Minimization of Motor Detent Torque Alignment Concept Based on the existing tolerance chain between Drive Unit and Base Plate, Drive Shafts and Reflector and between Base Plate and Feed Horn (Mounting Brackets), the implementation of a suitable alignment concept was mandatory in order to fulfil the pointing and performance requirements. In order to cope with the schedule constraints during the integration and test phase, it would have been favorable to avoid as far as possible a time intensive alignment concept. For example, concepts using in situ shimming and adjustment of the individual components during the integration and test process are time and effort intensive. Therefore, two alignment alternatives were discussed in this context: one was to manufacture the relevant mating parts with sufficiently high accuracy in order to avoid shims wherever possible. This alternative was found not to be adequate, since the involved tolerance chains did not allow to manufacture the individual parts with sufficiently high precision without high additional effort. The second alternative was to provide active adjustment and alignment provisions already by design, so to allow alignment by means of suitable adjustment screws after integration. This alternative was skipped due to the fact that it added high design complexity, imposed stiffness and load capability limitations and would have increased mass and moment of inertia. Therefore it was decided to go for a conventional shimming approach and to adjust first the Reflectors about two axis in the interface between Drive shaft and Reflector and then to shim the feed horn support structures with respect to the Reflectors. The correct Reflector alignment with respect to the feed horn was supported by using Reflector best fit analysis data as an input for the 3D measuring machine during the reflector alignment process. A zero referencing possibility in rotational direction was additionally implemented in the electronics command interface in order to allow for compensation of rotational misalignment of the Reflectors between the S/C mechanical and electrical zero. The observed phenomenon was a randomly occurring incorrect start command execution of the scanning function after switching from the redundant to the main path. After detailed check of the electronics function and also of the mechanism integrity, the detailed root cause investigation led to the suspicion that the error must be produced by the power supply used during equipment test. It was proven by test, that the probability to reproduce the random error was depending on the actually used power supply unit. Therefore the power supply characteristics were investigated in detail and it was found that the encoder supply voltage (5 V) provided to the encoder had a rise time of >20 ms. As a consequence a switch box was integrated into the output line of the power supply so to allow switching the encoder voltage by a separate command after switching on the power supply in order to guarantee a voltage rise time of < 5 ms. Scan Performance during Ground Test the key functional performance requirements of the Antenna Scan Mechanism are its high velocity constancy during the earth scan period and the requested minimum time consumption for the motion time between two earth scans (hot/cold calibration and movement between these positions) in order to maximize the useful observation time. This was achieved by optimizing the motor dimension and its output torque and dynamics in combination with a minimized moment of inertia of the rotating masses. The achieved measured velocity and acceleration profile of two subsequent scan periods is shown in Figure 11. The maximum angular velocity is about 9 rad/s, the maximum achieved acceleration is about 2 2 150 rad/s while the maximum deceleration is up to 180 rad/s (deceleration is supported by bearing friction torque). Measured Performance Data (Velocity and Acceleration) Orbit Performance the temperature variation of the mechanism over the orbit was analyzed during the development phase. The housekeeping data obtained during the mission show good correlation to the analysis. An active thermal heater concept for the instrument is not needed due to a trimming radiator. In Figure 12, the average current needed to drive the scan mechanism is plotted over time. Since the current needed to drive the system is a good indicator of the mechanism health status and especially of its bearings, such data are extremely helpful to gain information for similar flight designs requesting non uniform bearing rotation. The overall number of scans performed within the time frame shown in Figure 12 amounts to about 16. Conclusions and Lessons Learned Electron beam welded connections (electron beam) were found to be not adequate for the application and should be carefully investigated in view of their load capability and durability under the given vibration loads. Alignment concepts using accurately manufactured parts provide schedule advantage over alignment concepts using shimming methods, however depending on tolerance chains they are often hard to be realized. Therefore, the conventional in situ shimming method using shim washers during integration and test process was found to be the most effective one. The detent torque of the motor using two independent motor stators could be reduced by turning one of the redundant motor stators by half a stator slot pitch with respect to the other in order to smoothen the overall detent torque amplitude. The output characteristics (voltage rise time) of power supplies might be important for the correct operation of sensitive equipment. The voltage rise time of power supplies and potential requirements from equipment side should be carefully cross checked before using standard power supplies on sensitive equipment. The drive concept using liquid lubrication and two pairs of thin ring ball bearings in face-to-face arrangement provides good life performance at continuous extreme acceleration / deceleration conditions as in the presented application. Based on the available current housekeeping data, the current is very stable over time and no bearing degradation which would result in a higher torque /current level is observed after 2 years of continuous scanning operation (24 million revs). From the very beginning, it was clear that the jitter and pointing performance could only be realized by minimizing friction and stick-slip effects. The mirror units were designed to exhibit minimum susceptibility towards thermo-mechanical disturbances. While being of pure Beryllium for weight reasons, the design solution eventually chosen was a highly optimized mirror shape on an innovative iso-static mounting construct. The high structural loading capacity while maintaining a mass as low as possible was achieved by using AlBeMet or Titanium for all major structural parts. The entire terminal is a highly complex system consisting of tightly interacting subsystems involving mechanical, thermal, optical, and electro-optical elements. The relative velocities of the involved communication terminals may be quite high. With mutual line of sight contact limited to as little as 20 minutes fast beam acquisition is crucial. This furthermore, dictates the need for a high-pointing accuracy even at moderately high-speeds. Low Jitter: Maximization of the transfer power is essential to maintaining high data throughput. Furthermore, thermo-mechanical stability throughout the operation at these temperature extremes must be guaranteed. Thus, radiation hardness of the equipment must be very high, which reduces the number of choices for electronic components and surface coatings of mechanical or optical parts, or may even impose the need for shielding. High Load Capability: To enhance versatility and extend the scope of application, the quasi-static loads have been chosen accordingly. Making use of significant synergies, the two Actuator Assemblies have been designed to be identical. Typically, the first point can be reached through a soft and low preloaded bearing system (see Ref. However, this is in contradiction to the last point, which generally asks for stiff, highly preloaded systems preventing too much gapping in the bearings. The struts also serve to synchronize the motion so that the parallelism of the axial motion of the upper and lower bearing housing is extremely high. In the high-preload state, it provides high stiffness for launch in order to prevent bearing gapping, a concern for bearings of the highest surface finish quality, and in order to protect the close clearance between the rotating and static discs of the high precision encoders from touching. Finally, the actuator units are equipped with 24-bit Optical Encoders from Codechamp, which allow for a very smooth control and hence contribute to the achievement of the jitter requirements in motion direction. Cable Wrap A major challenge for many multi-axis motion systems, especially with large angular motion ranges, is the transmission of power and signals over one rotation axis to the next. In order to keep the design simple and close to previous heritage, a flex print design has been utilized in Omega configuration (see also Ref. One advantage of this design is that the power lines and the sensitive encoder signals can be routed over different ribbons, providing naturally better protection from interference. Hence, lateral accelerations can cause rotational movements, which need to be prevented. In addition, the latch positively preloads the Elevation structure into the flex supported contacts on either side, which thus stop rotational motion around the Elevation Axis. Launch Lock Optical Elements Along with the mechanization units, the performance of the mirrors is of critical importance. The key performance characteristics of the optical coating are high reflectivity in the target frequency band (>99. One particularly noteworthy aspect of the mirror units is the iso-static mounting concept. While providing the necessary stability, stiffness, and strength for the high launch loads, the mounting concept also provides thermal decoupling and by this means high tolerance towards thermo-mechanical influences. Thereby, the establishment of stable processes for black Titanium and black Nickel on AlBeMet proved to be veritable challenges. Figure 8 shows that the bearing system, running at low preload, has a mean resistive torque of < 0. Torque and Torque noise measurements Figure 9 shows the achieved in plane and out of plane random vibration input levels: Figure 9.