bluuebunny/crossref_metadata_2025 huggingface dataset:
Internal Aerodynamics Problems
Authors: Livesey J. L.
Published: July 2016

This paper defines Internal Aerodynamics and via similarity generalises the concept to include internal flows of fluids other than air.

Variable area ducted flows are considered distinguishing one, two and three-dimensional treatments and the difference between accelerating and diffusing flows is stressed. The design of variable area ducts using ideal inviscid fluid theory, ideal fluid plus boundary layer theory and inviscid but rotational fluid theory is discussed. The success and limitations of these theories with reference to contractions and diffusers is surveyed The particular difficulty of a diffusing flow as affected by entry velocity profile and turbulence is considered.

From the problem of simulating entry velocity profiles arises the need for the generation of required velocity profiles in duct systems. Examples of methods of generation and difficulties are discussed.

Next follows a series of examples of internal flow problems.

The radial flow diffuser is considered as an example of the interaction of viscous and inertia effects. An approximate theoretical treatment is given and the real flow, with the occurrence of reverse transition, is described.

The deliberate production of a reversed flow regime for flame stabilisation is described with reference to a marine boiler register Aspects of pressure drop and stability are considered.

Secondary flow is defined and the origin in the distortion of the upstream vorticity field is described. The case of a strut wall junction is given with details of the downstream flow where the secondary flow produces apparent multiple wakes from a single strut.

Air flow excited vibration of heat exchanger tubes is described. Different mechanisms resulting in transverse or streamwise oscillations and the coupled modes of tube rows are discussed.

Finally the paper emphasises the large available body of information in internal aerodynamics, largely of aeronautical origin, and considers its usefulness and limitations for the problems discussed.
Early Days with Aircraft Design and Development
Authors: Jones T.
Published: July 2016

In my boyhood days I well remember seeing balloon ascents at the Crystal Palace, which sowed the seed for my ideas of man being supported and carried in the air. Many times, when flying my kite, it passed through my mind that if, instead of holding it against the wind to keep it in an elevated position, the kite would rise and keep elevated if it were moved through the air at a speed equal to that of the wind, but this boyish reasoning into matters of heavier-than-air flying machines remained dormant while I carried on with my general engineering training.

Between the years 1905 and 1910, I took serious notice of the experiments made with gliders, particularly those by Wilbur and Orville Wright. Thus, my interest in aviation was revived, and with the experiments with engine-powered gliders, and the very early flying machines, I definitely decided that Aviation was to be my future occupation.
Special Problems in the Military Field
Authors: Poulton E. A.
Published: July 2016

When I was first asked to take part in this Colloquium I declined on the grounds that there had been too many reliability conferences already, and I feared that another would only take the time of good engineers off their day to day tasks of improving the reliability of British products. Having heard some of the contributions, I think I should revise that opinion. We have heard some good material. I was prevailed upon to say a few words on the problems of military aircraft and this I will do. I shall omit almost entirely references to equipment because, as I see it, the problems on the equipment side are fairly similar whether the aircraft is a military or a civil one.
A Simple Correlation of Turbine Efficiency
Authors: Smith S. F.
Published: July 2016

For a number of years it has been the practice at Rolls-Royce to determine the basic aerodynamic characteristics of the turbines of our engines by tests of model turbines. The first model of the single-stage Derwent I turbine was tested In 1945 and a design point efficiency of 75 per cent was measured. Since then over 600 different turbine configurations have been tested and many of the more recent turbines have achieved efficiencies appreciably better than 90 per cent. Typical of modern turbines is the Spey two-shaft turbine in which the four stages reach a design point efficiency of a little over 92 per cent. This paper presents a description of the test techniques which are used in this work and also a simple method of correlation which relates the efficiency of some 70 turbine stages to the velocity triangles and enables the efficiency of those turbines, which fall within the scope of the correlation, to be predicted with an accuracy better than ± 2 per cent. The measured value of turbine efficiency can be markedly influenced by the measurement technique, so the way in which the turbines are manufactured and tested is described in some detail.
The British Army Unit Light Helicopter Project
Authors: Crookenden N.
Published: July 2016

The revival of flying in the British Army dates from the Air OP flights of the Second World War, manned jointly with the RAF and highly successful in their limited role. In 1957 the Army took over full responsibility for its own aviation and in the previous year had already agreed with the Air Ministry and the Ministry of Supply to purchase the Saunders-Roe Skeeter. This two-seater aircraft had been under development since 1948. It was designed for worldwide use and with its 215 hp Gypsy Major engine it was supposed to have a service ceiling of 10 000 ft and an ability to climb at 180 ft/min outside ground effect at 4000 ft and ICAO + 30°. By 1958 the Skeeter had been accepted into service, but on its tropical trials in Aden in 1959 and 1960 it could produce only marginal power and the cylinder head and oil temperatures were above limits. It was therefore relegated to use in temperate climates and the Army was faced with the situation of still having no helicopters deployed in the Far East and Middle East. We had to make do there with the Auster, a fine, if rather senior reconnaissance aircraft, able to carry out only a few of the many roles required of an Army aircraft. A new aircraft, the Saunders-Roe P531, which became the Westland Scout, was ordered in 1959.
Hovercraft Noise and its Suppression
Authors: Richards E. J. , Sharland I. J.
Published: July 2016

Although the science of Hovercraft is still in its infancy, sufficient promise is already being shown to indicate a commercial and military future as alternative means of transportation. Since transportation involves power, and power involves noise, it is imperative that even at this early stage, development does not proceed in a direction which involves excessive noise and in so doing builds up the embarrassing situation for itself of the kind now occurring with aircraft at London Airport.

To give an example, one of the major problems in establishing a third airport for London is obtaining a quick method of communication between such an airport and the centre of the city. Unless this can be achieved, the advantages of supersonic travel will be nullified. The roadways and railroads are already full and alternative forms of travel must be found.
Airline Engineering and Maintenance: Reduction of Costs by Job Control and Time Standards
Authors: Bennett W. L.
Published: July 2016

Is there a danger of trying to over-simplify the manner in which costs can be reduced? Has the colour grey been deleted from our dictionary, and is everything really black or white? It would seem to me there is a tendency for the technical man to over-rule completely the practical man or vice versa, and maybe there is room for the colour grey to return and be high-lighted in our dictionaries.

A number of subjects come readily to mind where, in my opinion, neither the purely theoretical nor the purely practical approach can achieve the best results, and the only efficient way is a combination of both. Job control and time standards is, I consider, a subject which comes into this category.
The Diffuser Inlet Flow Parameter
Authors: Cockrell D. J. , Diamond M. J. , Jones C. D.
Published: July 2016

In the establishment of a fluid circuit's behaviour, it has been shown that the condition of the entry flow into each component of the circuit is of significance. This note indicatesthe problems encountered by a designer using diffusers at the present state of knowledge, and outlines a hopeful method of reducing diffuser pressure losses.
On the Bending of Clamped Skewed Plates Under Uniform Pressure
Authors: Kennedy J. B.
Published: July 2016

A simplified approximate solution for clamped skewed plates under uniform pressure is presented. Variations in maximum edge and centre moments with skew angle and sides ratio are shown plotted. The convergency of the solution is checked and results compared with the limited available data. Results were verified by an experimental investigation.
Assessment of Thermal-Fatigue Resistance of High Temperature Alloys
Authors: Coles A. , Skinner D.
Published: July 2016

Conditions of thermal fatigue encountered in the Aircraft Industry are usually located in engine components subjected to severe temperature and stress cycling. These components include gas turbine blading, nozzle guide vanes, flame tubes and turbine discs fabricated from a number of different materials ranging from Nimonics to sheet iron— and cobalt-base alloys. In recent years considerable experimental work has been carried out to assess material behaviour under thermal fatigue conditions and several means of testing have emerged. Rapid heating and cooling cycles using a “fluidised bed” technique have been extensively applied by Glenny and co-workers, at NGTE, and by material manufacturers to aid alloy development. Other experimenters have used axial straining devices based on expansion and contraction of heated columns followed by air cooling. One aircraft engine manufacturer has developed a thermal fatigue rig incorporating a repeated tensile axial load and temperature cycle. A further means of assessment has been developed by Forrest at NPL, in which the test specimen is strain cycled under reverse-bend conditions at constant or fluctuating temperatures.
The Calculation of the Discharge Coefficient of Profiled Choked Nozzles and the Optimum Profile for Absolute Air Flow Measurement
Authors: Stratford B. S.
Published: July 2016

A choked nozzle with an appropriate wall contour has adischarge coefficient, CD, so close to unity that a theoretical calculation of (I—CD) would allow the nozzle to be used as an absolute meter for air flow. The high discharge coefficient results basically from the fact that ∂(ρv)∂p=0 at M=1.

Simplified calculations yield formulae for the boundary layer displacement thickness and for the flow reduction resulting from the variation in static pressure across the throat. The optimum profile for the wall at the throat of an absolute meter is suggested to be a circular arc of radius of curvature equal to about twice the throat diameter. For such a meter the theoretical discharge coefficient is found to be within ¼ per cent of 0·995 over a wide range of Reynolds numbers.

The uncertainty in the discharge coefficient for a steady flow at Reynolds numbers of 106 and over appears to be less than ±0·15 per cent, both when the boundary layer is known to be entirely turbulent and when it is known to be entirely laminar. When the state of the boundary layer is not known the corresponding figure appears to be ±0·25 per cent. Experimental information might therefore be helpful on transition—under the appropriate conditions of flow unsteadiness and rig vibration. Available experimental results with known boundary layers tend to confirm the theoretical discharge coefficients down to a Reynolds number of 0·4x106.

A pressure ratio of about 1·1/1 or less would probably be sufficient to establish fully supersonic flow if the nozzle were followed by a suitable diffuser.
On the Bending of Rectangular Orthotropic Plates with Small Initial Curvature
Authors: Rajappa N. R.
Published: July 2016

Bending analysis of rectangular orthotropic plates due to lateral loads has been considered by many writers. A small initial curvature has no effect on the bending of a plate due to the action of a lateral load, and the final deflection curve may be obtained by superposing the ordinates due to the initial curvature on the deflections calculated as for a straight plate, but when the plate is subjected to compressive forces acting in the plane of the plate, the initial curvature influences considerably the deflections produced by these forces. The analogy between bending of orthotropic plates with small initial curvature and the plate vibration is established here by expressing the ratio of the initial deflection to the additional deflection in terms of the frequencies of free vibration.
The Investigation of Aircraft Accidents With Particular Reference To Those Caused By Mechanical Failure, Their Diagnosis And Lessons Learnt From Them
Authors: Newton E.
Published: July 2016

Since the mythical dawn of man's attempt to emulate birds and fly, and some believe this started with Icarus, man has been frustrated by his apparent inability to predict or prevent occasional disaster arising from failure of his mechanical aids to flight. From ancient Icarus with his ultimate and disastrous thermal structural failure, to the present and future aircraft the same problem although now in a more sophisticated and complex form, confronts the aircraft designer and engineer of today.

This paper is not intended to be a comprehensive treatise on Aircraft Accident Investigation as a whole because this is a subject of many facets and problems, but rather is it intended to draw attention in basic and elementary form to some types of mechanical failures or inadequate design criteria which have caused accidents to aircraft in the past, the methods used in their diagnosis and, what is perhaps more important, some lessons that have been learnt from them.
The Wallis Ultra-Light Autogyro
Authors: Wallis K. H.
Published: July 2016

The speaker has no specialist knowledge of agricultural aviation and will therefore briefly describe the aircraft, and provide thoughts on possible uses in aid of agriculture.

The ultra-light autogyro is probably the smallest practical aircraft of any type. Happily it does not need to be correspondingly fragile or delicate and it is little affected by turbulence or inclement weather, in the air or on the ground.

Some thought has already been given to an agricultural autogyro, although a somewhat larger machine than the Wallis autogyro was envisaged. While advantages would undoubtedly ensue from the larger size, such an aircraft would probably be in competition with comparable helicopters and fixed - wing machines. By the time development was complete there might be no great saving in first cost or maintenance.
Lift Produced by a Sonic Boom
Authors: Sigalla A.
Published: July 2016

The Technical Note by C. H. E. Warren in the September Journal raises a question on the transfer of lift, of an aeroplane in supersonic flight, to the ground. This problem was considered in reference 2. It was shown that, as expected, the resultant of the pressure field produced by the aeroplane is equal to its lift. This apparent inconsistency with the N-wave pattern, predicted by Whitham stems from the fact that most applications of Whitham's theory are based on asymptotic forms for the velocity perturbations. Thus, the formula for the axial velocity perturbation is obtained by allowing (M2— l)l/2r/y to tend to infinity, where M is the flight Mach number, r the radial distance away from the aeroplane, y=x—(M2 — l)1/2, and x is the distance along the aeroplane flight direction. This approximation is valid in the vicinity of the shock waves emanating from the aeroplane.
Aquaplaning on Runways
Authors: Trollope D. H. , Wallace K. B.
Published: July 2016

We have followed with considerable interest the two recent technical notes that have appeared in the Journal on aquaplaning (Mr. Gadd, p. 189, March 1963 and Mr. Gray, p. 302, May 1963). May we take this opportunity of drawing to your attention some work on this topic which has been carried out in the Civil Engineering Department of the University of Melbourne in co-operation with the Department of Civil Aviation, Commonwealth of Australia?
The Airlines’ Point of View
Authors: Marking Henry
Published: July 2016

My Talk will be Brief because Mr. Kean has covered the field extensively and extremely well.

What is Interchange? Mr. Kean indicated that it is not a very satisfactory description of what takes place because it is not a word which describes it accurately, and I think a good deal of confusion about interchange exists in the minds of many laymen because, unlike most air transport words which had their roots in surface transport, interchange so far as I know is peculiar to air transport; hence people are apt to think that it is something special, and that special rules must apply to it. In fact I suggest that it is nothing of the kind; all it is is a certain kind of charter, and the same rules apply to interchange of aircraft as to any other kind of charter, and the reason that it has been singled out as a special problem for lawyers is that its characteristics make it extremely difficult to work satisfactorily, internationally particularly, if the normal rules are applied.
Optimum Elastic Restraint for Pressurised Circular Plates
Authors: Bert Charles W.
Published: July 2016

For uniform-thickness, solid circular plates made of isotropic elastic material and elastically restrained at the edge, expressions are derived for the optimum support stiffness to minimise the following quantities:

1.

The largest effective stress based on several different strength theories.

2.

The largest effective stress per unit of maximum deflection or per unit volume displaced.
Education of the Airline Engineer
Authors: Walls A. J.
Published: July 2016

Mr. Wilkinson's paper (July 1963 Journal, pp. 421-6) will doubtless be universally applauded by airline management. One can only hope that it receives equal attention from those responsible for the education of Graduate Engineers.

His point about economic training is basic. It is extraordinary how, as professions evolve, certain fundamentals appear to be lost. From the earliest days of Engineering, an Engineer was denned at “a man who could do for a penny what any fool can do for twopence.” I think if the point were raised with most Engineers they would all admit that economy is at the very root of the profession. Nevertheless, how true Mr. Wilkinson is when he points how that Engineers receive little or no formal economic training in their basic education.
Study of the Human Pilot as a Servo-Element
Authors: Hall I. A. M.
Published: July 2016

A method for describing the action of a pilot in mathematical terms is presented. The method applies for tracking tasks and gives a pilot describing function which can be used in conventional servo-analysis. Flight simulator data obtained in this way for a wide variety of aircraft longitudinal response characteristics are presented and the effect of these characteristics on the pilot's action is discussed fully. In order to illustrate that work of this kind can lead to a quantitative understanding of pilot's “handling qualities” opinion, the recorded pilot opinions are “predicted” from a knowledge of three simple aircraft characteristics.
Powered-Lift Research at Langley Field
Authors: Gustafson F. B.
Published: July 2016

The title of this paper permits considerable latitude; also, there have been several previous papers on rather similar subjects. It seems best to explain therefore that the two primary purposes of this paper are, first, to bring the entire VTOL coverage of NASA's Langley Research Center up to date; and, second, to review a segment not covered in the references mentioned, namely, helicopter research. Also included are background history, and indications of the direction in which the research seems headed.
Atmospheric Turbulence on South African Air Routes
Authors: Halliday E. C. , King J. A.
Published: July 2016

When South Africa joined the Commonwealth Advisory Aeronautical Research Council in 1948 it was decided that the study of atmospheric turbulence was the first research project which could be undertaken. Equipment for the recording of aircraft accelerations was not then available commercially so an apparatus was assembled in the laboratory of the National Physical Research Laboratory, use being made of a commercial sensing head and an oscillograph galvanometer with photographic recording. The apparatus weighed about fifteen pounds so it was used on Douglas DC-3 (Dakota) aircraft which were flying for the S. A. Air Force on routes from Pretoria, to Durban, Cape Town and return. This apparatus recorded altitude and vertical acceleration of the aircraft. At a later date a lightweight commercial instrument was purchased and fitted into a Douglas DC-4 (Skymaster) aircraft flying on the routes of S. A. Airways. This instrument recorded altitude, air speed, and vertical acceleration.
The History of the Lecture Theatre
Authors: Moult E. S.
Published: July 2016

The lecture theatre has now been opened, and I have taken it on myself to be the first to give an address in this newly-opened Theatre. I think this occasion is opportune to tell you something of its history and, in so doing, to demonstrate some of its facilities.

For many years the Council of our Society has considered the possibility of the Society having a Lecture Theatre of its own. Many of our Past-Presidents and Councils have expressed the desire and have made explorations but, though the wish was there, we did not see the means. Recent increases in the activities of the Society, the creation of Sections and Groups, each with its own Lecture Programme, added a new emphasis. Moreover, the problem of the hiring of halls has become increasingly difficult when one remembers that the Programme in London alone now includes more than 60 lectures.
The State of the Art in Management Education Applicable to Aerospace Activities
Authors: Connolly J. V.
Published: July 2016

During the past two years, there has been a sharp acceleration to the interest which industry has displayed in the subject of management education. This can be attributed to these factors: —

(a) A more widespread realisation of the gap developing between the UK and a number of foreign economies, as manifested by diverging rates of the major economic indicators.

(b) The attainment of top-management responsibilities by a younger generation of managers, many of whom had been given some earlier training and who were more conscious of its value than the incumbents of the job from earlier generations.

(c) The publication of the Franks, Robbins and (in the aerospace industry) the Plowden reports.

(d) The impact of the Industrial Training Boards making it manifest, in terms of serious levies, that training was an economic necessity and therefore must be investigated thoroughly.

Notwithstanding the widespread awakening of interest, it is very belated and sets numerous problems. The problems are in two areas—scale and quality.
Birds and Aircraft: A Problem at Auckland’s New International Airport
Authors: Saul E. K.
Published: July 2016

Summary:—

The bird hazard to aircraft at Auckland International Airport, Mangere, NZ (Lat 37° 00’ 30” S, Long 174° 47’ 30” E) is examined. Geographical features affecting the hazard are explained and the history of the hazard recounted, and the groups and component species of birds, their daily movement patterns and seasonal abundances discussed. The greatest potential danger is from the waders, but gulls are the greatest actual danger possibly because gulls live irregular, opportunistic lives in comparison with the strict, tide-governed existence of the waders. An analysis of the bird incident figures for a year tends to confirm this view, in spite of the comparative rarity of incidents.

Measures taken or projected against the birds are reviewed. Special reference is made to unorthodox methods—the provision of alternative high water roosting sites, experiments with a radio-controlled model simulating the hawk shape, and the use of gull corpses as scaring agents. While worthwhile reductions have been made to the hazard, continued work and constant vigilance is necessary.
Shock-induced separated flows on the lee surface of delta wings
Authors: Seshadri S. N. , Narayan K. Y.
Published: July 2016

Experiments were conducted to study shock-induced separated flows on the lee surface of delta wings with sharp leading edge at supersonic speeds. Two sets of delta wings of different thickness (10° and 25° normal angle), each with leading edge sweep angles varying from 45° to 70°, were tested. The measurements, carried out in a Mach number range from 1.4 to 3.0, included oil flow visualisations (on both sets of wings) and static pressure distributions (on the thicker wings only). Using the test results, some features of shock-induced separated flows, including in particular the boundary between this type of flow and fully attached flow, have been determined. The experimental results indicate that this boundary does not seem to show any significant dependence on wing thickness within the limit of thicknesses tested. It is shown that this boundary can be predicted for thin delta wings using a well known criterion for incipient separation in a glancing shock wave boundary layer interaction, namely that a pressure rise of 1.5 is required across the shock. Comparison of the predicted boundary with experimental results (from oil flow visualisations) shows good agreement.
British Universities and Aeronautical Research|The Fourth Lanchester Memorial Lecture
Authors: Young A. D.
Published: July 2016

Some remarks are first made on the pertinence of the topic chosen for a lecture dedicated to Dr. Lanchester. A brief historical review is then given of the development of University teaching and research activities in Aeronautics from the early years of the Century to the present. An imaginary but typical modern University Department of Aeronautical Engineering is described with particular reference to numbers of students, staff, laboratory equipment and budget. Some of the many research topics to which the Universities have made and are making important contributions are then discussed briefly. These are to illustrate the scope and tendencies of University research against the background of current developments in Aeronautics. Among the subjects referred to are such topics as the structure of the turbulent boundary layer and the measurement of skin friction, flow Separation phenomena, boundary layer drag and heat transfer at high speeds, aeroelasticity, the application of matrix methods to structural analysis using digital Computers, structural damping, secondary flows in propulsion machinery, the rotating stall and jet noise.

The paper concludes with some general remarks on the relationships between the Universities, the Government Research Establishments and the Industry and on the future of University research. The importance of maintaining on the one hand the independence of the Universities and on the other hand the closest contact between them, the Government Establishments and Industry is strongly emphasised.
Ballistic Research Rockets With Particular Reference to Black Knight
Authors: Lyons D.J.
Published: July 2016

The 1172nd Main Lecture to be given before the Society and the 41st to be held at a Branch centre “Ballistic Research Rockets with Particular Reference to Black Knight” was given under the auspices of the Luton Branch on 1st December 1960. Mr. F. H. Pollicutt, F.R.Ae.S., Chairman of the Luton Branch opened the meeting by welcoming the President, Dr. E. S. Moult, C.B.E., B.Sc., F.R.Ae.S., M.I.Mech.E., the other members of the Council of the Main Society who were present, and representatives from the Bristol, Birmingham and Wolverhampton, Coventry, Christchurch, Derby, Hatfield, Halton, Henlow, Preston and Weybridge Branches. He then asked Dr. Moult to preside over the rest of the proceedings.

Dr. Moult expressed his pleasure at being present on this occasion–the second time a Main Society Lecture had been presented at the Luton Branch–and then introduced the Lecturer, Mr. D. J. Lyons. Mr. Lyons took his degree in Aeronautical Engineering at Queen Mary College and subsequently joined the Wind Tunnel staff at Farnborough. During the war he became a flying instructor in the R.A.F. and later rejoined the Aerodynamics Flight Section at. the R.A.E. For the next ten years Mr. Lyons was engaged in Flight Research on stability and control. In 1951 he was appointed Superintendent of the Experimental Projects Division in the Guided Weapons Department and in 1955 was promoted to his present position as Senior Superintendent of the Ballistic Missile Group of the Guided Weapons Department. He had been responsible from the Ministry aspect for the research and development connected with the Black Knight and Blue Streak Missile systems.
Airships
Authors: Pugsley Alfred
Published: July 2016

The first well-formulated scheme for lighter-than-air transport was put forward by Francesco de Lana-Terzi in a scientific treatise in 1670. He visualised a craft made lighter than air by evacuating the air from within it, and conducted the first accurate experiments to determine the density of air, which he found to be 1/640th that of water. It comes to most of us today as surprisingly relevant to recall why he did not carry his idea into practice: he was a Jesuit priest and wrote, in the words of Robert Hooke's translation, “God would not suffer such an invention to take effect, by reason of the disturbance it would cause to the civil government of men. For who sees not that no city can be secure against attack …“.
Early Research at Farnborough and Felixstowe
Authors: Garner Harry
Published: July 2016

The Early experimental work at the Royal Aircraft Factory, South Farnborough (as it was called then) has been described by a number of people. There was no organisation in the First World War, as there was in the Second, for the use of scientific man power. The gravitation of scientists to the Royal Aircraft Factory can, I imagine, only be explained by the attraction of working in an unexplored field. The results of the impact of this remarkable group on the future of aeronautics in this country were enormous.

My own relatively late appearance at Farnborough, towards the end of 1916, was the result of a series of accidents.
Piston Engine Fuels
Authors: Bass E. L.
Published: July 2016

Little Attention was paid to the characteristics of the fuel for the early aircraft engines. They had available to them a gasoline primarily intended for automobile engines, the earliest of which used wick carburettors. These carburettors required a fuel of extremely high volatility and with the straight run gasolines available at the time, volatility could be related to specific gravity. The lower the specific gravity, the better the volatility and the requirement for low specific gravity endured for about the first twenty years of the life of the aircraft engine.
Sensitivity of hidden Markov models
Authors: Mitrophanov Alexander Yu. , Lomsadze Alexandre , Borodovsky Mark
Published: July 2016

We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.
Width of a scale-free tree
Authors: Katona Zsolt
Published: July 2016

Consider the random graph model of Barabási and Albert, where we add a new vertex in every step and connect it to some old vertices with probabilities proportional to their degrees. If we connect it to only one of the old vertices then this will be a tree. These graphs have been shown to have a power-law degree distribution, the same as that observed in some large real-world networks. We are interested in the width of the tree and we show that it is at the nth step; this also holds for a slight generalization of the model with another constant. We then see how this theoretical result can be applied to directory trees.
Rates of Growth in a Class of Homogeneous Multidimensional Markov Chains
Authors: González M. , Martínez R. , Mota M.
Published: July 2016

We investigate the asymptotic behaviour of homogeneous multidimensional Markov chains whose states have nonnegative integer components. We obtain growth rates for these models in a situation similar to the near-critical case for branching processes, provided that they converge to infinity with positive probability. Finally, the general theoretical results are applied to a class of controlled multitype branching process in which random control is allowed.
An analysis of transient Markov decision processes
Authors: James Huw W. , Collins E. J.
Published: July 2016

This paper is concerned with the analysis of Markov decision processes in which a natural form of termination ensures that the expected future costs are bounded, at least under some policies. Whereas most previous analyses have restricted attention to the case where the set of states is finite, this paper analyses the case where the set of states is not necessarily finite or even countable. It is shown that all the existence, uniqueness, and convergence results of the finite-state case hold when the set of states is a general Borel space, provided we make the additional assumption that the optimal value function is bounded below. We give a sufficient condition for the optimal value function to be bounded below which holds, in particular, if the set of states is countable.
Study of a Stochastic Failure Model in a Random Environment
Authors: Cha Ji Hwan , Mi Jie
Published: July 2016

Most devices (systems) are operated under different environmental conditions. The failure process of a system not only depends on the intrinsic characteristics of the system itself but also on the external environmental conditions under which the system is being operated. In this paper we study a stochastic failure model in a random environment and investigate the effect of the environmental factors on the failure process of the system.
Optimal Control of a Large Dam
Authors: Abramov Vyacheslav M.
Published: July 2016

A large dam model is the object of study of this paper. The parametersLlowerandLupperdefine its lower and upper levels,L=Lupper-Lloweris large, and if the current level of water is between these bounds, the dam is assumed to be in a normal state. Passage across one or other of the levels leads to damage. LetJ1andJ2denote the damage costs of crossing the lower and, respectively, the upper levels. It is assumed that the input stream of water is described by a Poisson process, while the output stream is state dependent. LetLtdenote the dam level at timet, and letp1= limt→∞P{Lt=Llower} andp2= limt→∞P{Lt>Lupper} exist. The long-run average cost,J=p1J1+p2J2, is a performance measure. The aim of the paper is to choose the parameter controlling the output stream so as to minimizeJ.
Characterizations of Conditional Comonotonicity
Authors: Cheung Ka Chun
Published: July 2016

The notion of conditional comonotonicity was first used implicitly by Kaas, Dhaene, and Goovaerts (2000) and was formally introduced by Jouini and Napp (2004) as a generalization of the classical concept of comonotonicity. The objective of the present paper is to further investigate this relatively new concept. The main result is that a random vector is comonotonic conditional to a certain σ-field if and only if it is almost surely comonotonic locally on each atom of the conditioning σ-field. We also provide a new proof of a distributional representation and an almost sure representation of a conditionally comonotonic random vector.
Smile Asymptotics II: Models with Known Moment Generating Functions
Authors: Benaim Shalom , Friz Peter
Published: July 2016

The tail of risk neutral returns can be related explicitly with the wing behaviour of the Black-Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we establish, under easy-to-check Tauberian conditions, tail asymptotics on logarithmic scales. Such asymptotics are enough to make the tail-wing formula (see Benaim and Friz (2008)) work and so we obtain, under generic conditions, a limiting slope when plotting the square of the implied volatility against the log strike, improving a lim sup statement obtained earlier by Lee (2004). We apply these results to time-changed exponential Lévy models and examine several popular models in more detail, both analytically and numerically.
Markov Chains with Hybrid Repeating Rows - Upper-Hessenberg, Quasi-Toeplitz Structure of the Block Transition Probability Matrix
Authors: Dudin Alexander , Kim Chesoong , Klimenok Valentina
Published: July 2016

In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.
Optimal Co-Adapted Coupling for the Symmetric Random Walk on the Hypercube
Authors: Connor Stephen , Jacka Saul
Published: July 2016

Let X and Y be two simple symmetric continuous-time random walks on the vertices of the n-dimensional hypercube, Z
2

n
. We consider the class of co-adapted couplings of these processes, and describe an intuitive coupling which is shown to be the fastest in this class.
Continuous-State Branching Processes and Self-Similarity
Authors: Kyprianou A. E. , Pardo J. C.
Published: July 2016

In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.
On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications
Authors: Bercu Bernard , Cénac Peggy , Fayolle Guy
Published: July 2016

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of any even order converge in the almost sure central limit theorem for martingales. A conjecture about almost sure upper bounds under wider hypotheses is formulated. The theoretical results are supported by examples borrowed from statistical applications, including linear autoregressive models and branching processes with immigration, for which new asymptotic properties are established on estimation and prediction errors.
Stochastic Ordering of Exponential Family Distributions and Their Mixturesxk
Authors: Yu Yaming
Published: July 2016

We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general theorem based on the notion of relative log-concavity is shown to unify various specific results for the Poisson, binomial, negative binomial, and gamma distributions in recent literature. By expressing a convolution of gamma distributions with arbitrary scale and shape parameters as a scale mixture of gamma distributions, we obtain comparison theorems concerning such convolutions that generalize some known results. Analogous results on convolutions of negative binomial distributions are also discussed.
Importance Sampling for Failure Probabilities in Computing and Data Transmission
Authors: Asmussen Søren
Published: July 2016

In this paper we study efficient simulation algorithms for estimating P(X›x), where X is the total time of a job with ideal time T that needs to be restarted after a failure. The main tool is importance sampling, where a good importance distribution is identified via an asymptotic description of the conditional distribution of T given X›x. If T≡t is constant, the problem reduces to the efficient simulation of geometric sums, and a standard algorithm involving a Cramér-type root, γ(t), is available. However, we also discuss an algorithm that avoids finding the root. If T is random, particular attention is given to T having either a gamma-like tail or a regularly varying tail, and to failures at Poisson times. Different types of conditional limit occur, in particular exponentially tilted Gumbel distributions and Pareto distributions. The algorithms based upon importance distributions for T using these asymptotic descriptions have bounded relative error as x→∞ when combined with the ideas used for a fixed t. Nevertheless, we give examples of algorithms carefully designed to enjoy bounded relative error that may provide little or no asymptotic improvement over crude Monte Carlo simulation when the computational effort is taken into account. To resolve this problem, an alternative algorithm using two-sided Lundberg bounds is suggested.
A Random Multiple-Access Protocol with Spatial Interactions
Authors: Bordenave Charles , Foss Serguei , Shneer Vsevolod
Published: July 2016

We analyse an ALOHA-type random multiple-access protocol where users have local interactions. We show that the fluid model of the system workload satisfies a certain differential equation. We obtain a sufficient condition for the stability of this differential equation and deduce from that a sufficient condition for the stability of the protocol. We discuss the necessary condition. Furthermore, for the underlying Markov chain, we estimate the rate of convergence to the stationary distribution. Then we establish an interesting and unexpected result showing that the main diagonal is locally unstable if the input rate is sufficiently small. Finally, we consider two generalisations of the model.
On Consecutive Records in Certain Bernoulli Sequences
Authors: Holst Lars
Published: July 2016

In an infinite sequence of independent Bernoulli trials with success probabilities p

k
=a/(a+b +k-1) for k=1,2,3,…, let N

r
be the number of r≥2 consecutive successes. Expressions for the first two moments of N

r
are derived. Asymptotics of the probability of no occurrence of r consecutive successes for large r are obtained. Using an embedding in a marked Poisson process, it is indicated how the distribution of N

r
can be calculated for small r.
Generalized Increasing Convex and Directionally Convex Orders
Authors: Denuit Michel M. , Mesfioui Mhamed
Published: July 2016

In this paper, the componentwise increasing convex order, the upper orthant order, the upper orthant convex order, and the increasing directionally convex order for random vectors are generalized to hierarchical classes of integral stochastic order relations. The elements of the generating classes of functions possess nonnegative partial derivatives up to some given degrees. Some properties of these new stochastic order relations are studied. Particular attention is paid to the comparison of weighted sums of the respective components of ordered random vectors. By providing a unified derivation of standard multivariate stochastic orderings, the present paper shows how some well-known results derive from a common principle.
A stochastic differential reinsurance game
Authors: Zeng Xudong
Published: July 2016

We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.
A new look at transient versions of Little's law, and M/G/1 preemptive last-come-first-served queues
Authors: Fralix Brian H. , Riaño Germán
Published: July 2016

We take a new look at transient, or time-dependent Little laws for queueing systems. Through the use of Palm measures, we show that previous laws (see Bertsimas and Mourtzinou (1997)) can be generalized. Furthermore, within this framework, a new law can be derived as well, which gives higher-moment expressions for very general types of queueing system; in particular, the laws hold for systems that allow customers to overtake one another. What is especially novel about our approach is the use of Palm measures that are induced by nonstationary point processes, as these measures are not commonly found in the queueing literature. This new higher-moment law is then used to provide expressions for all moments of the number of customers in the system in an M/G/1 preemptive last-come-first-served queue at a time t > 0, for any initial condition and any of the more famous preemptive disciplines (i.e. preemptive-resume, and preemptive-repeat with and without resampling) that are analogous to the special cases found in Abate and Whitt (1987c), (1988). These expressions are then used to derive a nice structural form for all of the time-dependent moments of a regulated Brownian motion (see Abate and Whitt (1987a), (1987b)).
Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications
Authors: Zhang Zhengcheng
Published: July 2016

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.
Large Cliques in a Power-Law Random Graph
Authors: Janson Svante , Łuczak Tomasz , Norros Ilkka
Published: July 2016

In this paper we study the size of the largest clique ω(G(n, α)) in a random graph G(n, α) on n vertices which has power-law degree distribution with exponent α. We show that, for ‘flat’ degree sequences with α > 2, with high probability, the largest clique in G(n, α) is of a constant size, while, for the heavy tail distribution, when 0 < α < 2, ω(G(n, α)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, α) a large clique of size (1 − o(1))ω(G(n, α)) in polynomial time.
Double-Barrier Parisian Options
Authors: Dassios Angelos , Wu Shanle
Published: July 2016

In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.