bluuebunny/crossref_metadata_2025 huggingface dataset:
Wind-Tunnel Screens: Flow Instability and its Effect on Aerofoil Boundary Layers
Authors: Bradshaw P.
Published: July 2016

Morgan has described a spatial instability in the flow through screens or grids of small open-area ratio. Head and Rechenberg and others have observed large span-wise variations in the thickness and shear stress of nominally two-dimensional boundary layers on flat plates and aerofoils in wind tunnels. It now appears that these spanwise variations are caused by the instability of flow through the screens. The jets of air issuing from the pores of the screen attempt to entrain more air by the usual mixing processes, but can only entrain it from each other, so that groups of jets coalesce in rather random (steady) patterns determined by small irregularities in the weave. The resulting variations in axial velocity are virtually eliminated by the wind tunnel contraction, but variations in flow direction are not so greatly reduced: a theoretical analysis shows that the observed variations of boundary-layer thickness, which often reach ± 10 per cent of the mean, can be produced by directional variations in the working section of the order of ± 1/20 deg, with a spanwise wavelength of the same order as the boundary-layer thickness.
The Determination of Maximum Range for an Unpowered Atmospheric Vehicle
Authors: Bell D. J.
Published: July 2016

The problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.

The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.

The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.

It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.
Curved Beams
Authors: Mitchell C. G. B.
Published: July 2016

A type of structure for which no general method of analysis appears to be available is that of a curved beam of low torsional strength and stiffness supported by a torque box. This note outlines ways of analysing two simple cases.
The Visualisation of Mass Transfer Rate Around a Sphere
Authors: Lee K. , Barrow H. , Ryley D. J.
Published: July 2016

The purpose of this note is to report the results of an experimental investigation which was conducted to permit the local mass transfer rate around a sphere to be visualised. The present problem of mass transfer from a sphere had its origin in a study of the evaporation of a water droplet in a superheated steam atmosphere. Because of the small physical size of the droplet and the difficulty of measuring local mass transfer rates from the droplet surface, it was necessary to employ a large scale model to study local transfer rate around a sphere. It was considered that flow visualisation would afford at least a qualitative result of local mass transfer rate. In fluid mechanics studies, the flow visualisation techniques are well known. Such methods include the use of smoke filaments, tufts, or chemical coatings and so forth to provide information about the state of boundary layer over a solid surface, fluid particle paths and state of flow.
A Centrifugal Hypersonic Wind Tunnel Facility for Investigating Effects of Inertia on Ablating Bodies
Authors: Ford Joseph Scott , Horton Wilfred H.
Published: July 2016

A most important aspect of space technology is the development of methods for atmospheric re-entry. In this phase of flight very severe structural and material requirements exist. The origin of the problem lies in the intense aerodynamic heating which occurs as the body enters the denser regions of the atmosphere. High stagnation temperatures at the nose, shear effects in the boundary layer, radiation from the hot gas in the shock wave, and heat liberated by the recombination of dissociated and ionised gases give rise to conditions which will result in the destruction of the body unless some form of heat protection is provided.
Night Spraying
Authors: Ripper W. E.
Published: July 2016

My Subiect is a highly specialised and rather adventurous one—the practice of night spraying of trees and agricultural crops from aircraft.

It may sound hazardous, as it is, and of course it is at present only attempted when biological or climatic factors make spraying by daylight undesirable or ineffective. It is also dependent on a favourable terrain, and the development of better equipment. Where these conditions are fulfilled, in certain cases night spraying may become part of the armoury of a number of spraying contractors, mainly in Africa and America.
Research and Development of Chemical Distribution Equipment for Agricultural Aircraft in California
Authors: Akesson Norman B. , Yates Wesley E.
Published: July 2016

Following the Second World War, agricultural aircraft use increased rapidly in the United States, but appears to have levelled off in the past five years. California is one of the largest users of agricultural aircraft of any State, with an estimated 8 million acres treated per year. This figure includes all applications of insecticides, fungicides, and herbicides, plus seeding, fertilising, and defoliation of agricultural crops, grasslands and forest areas. Also, this figure represents acres covered and includes duplicated applications. Certain crops, such as cotton, may have as many as four or five separate treatments during the season.
The Pilot's Viewpoint —1
Authors: McMahon J. M.
Published: July 2016

The following are various aircraft requirements which, it can be said, a pilot considers in the course of his employment in agricultural aviation.

1.

Physical comfort.

2.

Accident protection.

3.

Operating, performance and flying requirements.

4.

Work capacity and operational efficiency.
Structural Fatigue and Other Airworthiness Aspects
Authors: Williams J. K.
Published: July 2016

In this paper the emphasis is on safety problems connected with the use of light fixed-wing aircraft for agricultural purposes. Most of the aircraft concerned are between 2000 and 6000 lb all-up weight and are single piston-engined types. About 97 per cent of all hours flown in agricultural aviation all over the world are by such small fixed-wing aircraft, the remainder by larger aircraft such as the DC-3 and helicopters.

The mass of statistics available on this type of flying is therefore confined to the small fixed-wing aircraft and since this type is obviously the most important with respect to this activity, then it is appropriate to concentrate on this type.
Structural Design
Authors: Atkinson R. J.
Published: July 2016

The objective of Structural Design is to provide the structure that will permit the aircraft, whether military or civil, to do its job most effectively, that is with the least total effort, spread over the whole life of the aircraft from initial design until the aircraft is thrown on the scrap heap. There is thus no all-embracing simple criterion by which the success of the structural design can be judged. It is not sufficient to believe that percentage structure weight is of itself an adequate measure of effective design, either of the complete vehicle or of the structure itself; a well-known example is the provision of increased aspect ratio at the expense of structure weight, which may give increased fuel economy in the cruise and reduction in the total aircraft weight. Nevertheless, percentage structure weight is a useful measure, provided its limitations are recognised.
Magnetic Suspension and Balance System for Wind Tunnel Application
Authors: Chrisinger J. E. , Tilton E. L. , Parkin W. J. , Coffin J. B. , Covert E. E.
Published: July 2016

In this article a magnetic suspension and balance system suitable for wind tunnel application is discussed. General considerations are presented that illustrate the nature of the problems to be solved as well as one solution of these problems.Finally some initial wind tunnel data are presented.
Buckling of Bars of Variable Rigidity with Varying Axial Load
Authors: Sundara Raja Iyengar K. T. , Anantharamu S.
Published: July 2016

The Evaluation of buckling loads of columns presents a difficult problem whose rigorous solution may be very difficult particularly when the variation of moment of inertia or the axial load does not follow a simple law. Hence approximate methods such as the variational and numerical methods will have to be employed. An approximate method is suggested in this note which offers a convenient method for the calculation of buckling loads of bars with any type of end conditions.
The Speed of Sound and Mach Number Effects
Authors: Bragg S. L. , Smith S. F.
Published: July 2016

In most aerodynamic problems the speed of sound, a, is naturally taken as or where p, ρ and T are static values, γ is the specific heat ratio and R is the gas constant. This particular speed, however, is specifically that of plane waves advancing uniformly into an infinite expanse of a homogeneous medium. There are many other situations where the medium is bounded or inhomogeneous, for instance, in which small pressure waves do not propagate at this speed relative to the medium. Phenomena such as choking can then be shown to occur, not when the flow velocity is exactly equal to but when it reaches the new wave speed appropriate to the local circumstances.
The Stiffening Effect of an Overhang in a Circular Plate
Authors: Mansfield E. H.
Published: July 2016

The problem considered is that of a circular plate which is supported along an internal concentric circle and subjected to uniform pressure over the area bounded by the support line; the outer edge of the plate is free. This form of loading and support is used in the testing of glass panels, where the rigidity of the panel is determined from a measurement of the central deflexion. However, the formula in current use does not allow for the stiffening effect of the overhanging outer annulus.
Braking Problems
Authors: Harben D. A. J.
Published: July 2016

In the art of brake design, many of the difficulties which existed in the past have now been overcome, and this is due largely to the wealth of experience obtained over a wide range of energy absorption rates and heat sink temperatures. Much of this experience has been obtained on brake test machines on which the essential aircraft braking conditions can be reasonably simulated on the complete assembly of wheel, tyre and brake.
The Engineering Reliability of Shaft-Driven Helicopters
Authors: Fitzwilliams O. L. L.
Published: July 2016

I am honoured to have been invited to give this Third Cierva Memorial Lecture on a subject which has a general application to all forms of aircraft, and which is central to any consideration of the future of the helicopter.

Reliability is a problem, the extent and urgency of which can only be appreciated fully and at first hand by the operator of a large fleet of aircraft, but most of the discussions and documents which have helped to lay the basis for this paper are not for general publication. I believe that this has helped me to concentrate on the essentials of the problem, but there is a danger that the simple arguments on which the paper is based may not carry the emphasis needed to convey to my colleagues the critical attitude of the operators.
Generalisation of the Condition for Waviness in the Pressure Distribution on a Cambered Plate
Authors: Angus Boyd E.
Published: July 2016

Recently some data from tests done on a cambered plate have been published. The shape of metal plate aerofoil tested matched that taken up by a flexible two-dimensional sail. The most striking result in the rneasurements was the waviness present near the leading edge in the upper surface pressure distribution. To find the theoretical conditions under which such a waviness would occur a parabolic skeleton aerofoil was investigated, as this shape differed little from the actual aerofoil tested.
Spar-Web Design in Relation to Thermal Stresses-The Corrugated Web
Authors: Williams D.
Published: July 2016

The possibilities of a vertically-corrugated web as a means of reducing thermal stresses naturally have for some time been generally appreciated by designers. The stress relief to be expected is examined in some detail here. It is shown that quite shallow corrugations can be effective in reducing thermal stress and that a flange-to-web connection at corrugation-pitch intervals can offer substantial advantages over a more continuous type of connection. Arguments are presented to show why straight-sided corrugations are superior to curved ones.
Bending of Plates Built into Boundaries Irregular in Plan : a Study by Analogy
Authors: Richards T. H.
Published: July 2016

There is a considerable body of literature which is concerned with plates having straightforward plan forms, for example circular and rectangular plates have been studied extensively. When the edges are irregular relatively little work seems to have been done, although plates having single notches have been studied and a useful bibliography is found in reference . As far as the present author is aware, the problem of plates built into irregular boundaries has not been tackled.
Design Charts for Estimating Turbulent Skin Friction Drag on Cylindrical Bodies with Tangent Parabolic or Ogival Fore-Bodies at Supersonic Speeds
Authors: Brewer R. A. , Seel M. W. R.
Published: July 2016

When estimating the skin friction drag on bodies of revolution at the project design stage, it is normal practice to use an “equivalent flat-plate” method. This calculation is simple and requires little time to perform. However, in the final design stage, when more accurate estimates of the skin friction drag should be made the “equivalent flat-plate” method is still used. More exact methods, which include pressure gradient effects, are very laborious if they are evaluated by hand calculators. Even if a digital computor is used to evaluate the more exact methods, the time required to perform the calculations is considerably longer than that taken to calculate the other forms of drag. For these reasons, the simple “flat-plate” method has long held favour with designers.
Stagnation Point Heat Transfer Measurements at Super Satellite Speeds
Authors: Offenhartz E. , Weisblatt H. , Flagg R. F.
Published: July 2016

Recent lunar and planetary return vehicle studies have stimulated interest concerning the effect upon stagnation point heating due to electronic heat conduction associated with re-entry at speeds greater than 30,000 ft./sec. In order to provide experimental data for comparison with theory, a series of experiments was undertaken in which shock tube techniques were utilised for the measurement of the stagnation point heating of a blunt body over a stagnation enthalpy (Hst/RT0) range of 650 to 900, corresponding to velocities between 32,000 ft./sec. and 39,000 ft. /sec. respectively. The tests were performed in a 1·5 inch diameter shock tube with 3 foot length driver and 16 foot length driven section.
The Story of Indian Air Transport
Authors: Tata J. R. D.
Published: July 2016

The Sixteenth British Commonwealth Lecture, The Story of Indian Air Transport, by Mr. J. R. D. Tata, Chairman of Air-India International, was given before a distinguished audience on 18th November 1960 at the Institution of Mechanical Engineers, Birdcage Walk, London, S.W.1.

The President of the Society, Dr. E. S. Moult, C.B.E., B.Sc., F.R.Ae.S., M.I.Mech.E., presided at the meeting. Before introducing the Lecturer the President explained that hitherto the election of Fellows had been initiated by the Council and announced once a year but, under the new By-Laws, Fellowship was to be regarded as a position which could be attained by any qualified member who had reached a position of eminence and responsibility in the profession of aeronautics. At the same time it had been decided that the announcement of such elections should be made not just once a year, but on occasions such as this.

The names of 22 members who had been elected to Fellowship since May 1960 were then read out by the Secretary. (These names were published in the December Journal–Ed.)

After congratulating the new Fellows, Dr. Moult said that the British Commonwealth series of lectures started at the end of the War in 1945, and had continued annually until the present day. Throughout the years they had had a series of outstanding lectures on subjects associated with aeronautics in the Commonwealth, given by most distinguished lecturers. The stature of this lecture was set for all time in 1954 when His Royal Highness The Duke of Edinburgh addressed them on “Aviation and the Development of Remote Areas”. Now they were to hear about the growth of aviation in one of the great members of the Commonwealth. Air Transport in India was now thirty years old1 and there was no one more suited to tell the story of that thirty years than their lecturer, Mr. J. R. D. Tata.

Mr. Tata had been actively associated with this development all his working life. Indeed, it was true to say he had had a major part in it. He learned to fly in 1929 and personally flew the first scheduled transport service in India in 1932. He had been associated with aviation throughout all these years and a few years ago was president of I.A.T.A., the International Air Transport Association; he was now Chairman of Air-India International. He had great pleasure in asking Mr. Tata to give the Sixteenth British Commonwealth Lecture, “The Story of Indian Air Transport.”
Lift Augmentation Ratio for Hovercraft
Authors: Carter A. D. S.
Published: July 2016

When hovercraft were first introduced the lift or thrust augmentation ratio was often used as a measure of their effectiveness. Although this ratio has been used less with subsequent development, it continues to be quoted in some literature. It is defined as the ratio of the hovercraft lift to the lift that would be obtained if the curtain jet were used to produce direct lift by jet reaction. An analytical expression is determined in outline.
Some Old Masters of the Society, and their Far-reaching Influence in Aviation
Authors: Gibbs-Smith Charles H.
Published: July 2016

Inventors who work in secret, and whose vital creations never see the light of day until the world has passed them by, are mostly figures of romantic fiction. Most inventors take good care that their devices are brought to public notice, preferably after patents have been granted to them; and one of their main concerns in the 19th century was therefore the channels of communication open to them.

Sir George Cayley wrote, in 1837, that “the experiments that have been made, and the investigation which it (the subject) has undergone, lie almost unconnected in the periodical publications of the last thirty years; and hence, every new speculator on the possibility of steering balloons takes up the subject merely on his own view”.
The Royal Aeronautical Society's Data Sheets
Authors: Cox H. L.
Published: July 2016

The origin of the Society's Stressed Skin Data Sheets was certainly my own paper, R and M No. 1553; it embarrasses me not at all to put it so. In 1930 the Structures Sub-committee of the ARC asked for a summary of the present state of knowledge regarding sheet metal construction, and the chairman, (Sir) William Farren, directed me as secretary to prepare a draft. I did so—the draft was discussed by the Sub-committee, revised and amended and finally in 1933 published over my name. To me the paper was a chore, albeit a welcome one, and all I myself really got out of it in the end was the realisation that I could do with a little more Anglo-Saxon: “What we know about …” would now be my title.
Aeronautical Research at the NPL
Authors: Nayler J. L.
Published: July 2016

In 1909, Sir Richard Glazebrook (then Dr.) was Director of the National Physical Laboratory and under him the Superintendent of the Engineering Division was Sir Thomas Stanton (then Dr.). These two scientists were responsible for initiating aeronautical research at the NPL. The main stimulus came, however, from the Advisory Committee for Aeronautics, formed in May 1909 with Lord Rayleigh as President and Glazebrook as Chairman. This committee obtained a grant from the Treasury for aeronautical work amounting to £1923 13s 5d for the seven months of that year, with a grant at the same rate for the year 1910; this money was spent at the NPL.
Recollections 1914–1934
Authors: Mckinnon Wood R.
Published: July 2016

The Outbreak of war in August 1914 naturally gave a fillip to the development of aeronautics and to building up research teams at the NPL and at the Royal Aircraft Factory at Farnborough. I was one of the earlier war-time recruits, in September 1914, engaged—after a mere assurance that I did believe in aeroplanes—by the enthusiast E. T. Busk, who was to lose his life so tragically when the BE2c he was flying caught fire on the 5th November 1914. At Farnborough I found a Cambridge contemporary of the Mechanical Sciences Tripos 1914, H. L. Stevens, who had joined before the outbreak of war, R. H. Mayo, Geoffrey Taylor, Melvill Jones, who had abandoned work on airships for Vickers, and F. M. Green from the motor trade on engines.
Aircraft Research Association Limited
Authors: Hills R. , Macadam E. J.
Published: July 2016

In the Years immediately following the Second World War, it became apparent that there was a lack of suitable wind tunnels in Great Britain to provide aerodynamic data at high speeds to meet all the needs of aircraft designers. The main firms had always had their own tunnels, but these were restricted in number and size because of the expense involved. Long-term research was carried out at the Royal Aircraft Establishment at Farnborough, but there was a need for a large-scale wind tunnel for more immediate development tests and especially for testing at transonic speeds.
British Aeronautical Research Facilities
Authors: Hilton W. F.
Published: July 2016

“And as in uffish thought he stood,The Jabberwock, with eyes of flame,Came whiffling through the tulgey wood,And burbled as it came!“

Scarcely has the final history of the steam train been written, than I am asked to write the history of the aeroplane, from the research facilities’ point of view. It can only be this nostalgia for the past which has enabled me to secure the willing help of so many people in the brief three and a half weeks allowed for the compilation of this paper. Of necessity it must be incomplete, but is, I trust, accurate.
Looking Backwards
Authors: Tiltman Hessell
Published: July 2016

Many others have told of the thrills of seeing the early flying machines leave the ground for the first time. I also was fortunate enough to see many pioneer flights at Colindale where I used to go during the school holidays; these flights absorbed my interest, and I suppose started me off with the thirst for aviation, which persisted throughout my later life. There is no doubt that the first twenty years of flying were the exciting ones, although we should probably be told that modern aeronautics has its own thrills—but different ones.
Memories of the Last Schneider Trophy Contests
Authors: Banks F. R.
Published: July 2016

My First active acquaintance with the Schneider Trophy Contests came in 1927 when I was chief experimental engineer to Peter Hooker Ltd of Walthamstow, generally known as the British Gnôme and Le Rhône engine company—since they had taken the licence for Gnôme engines as early as 1913. I was asked by H. C. Tryon, that grand experimental engineer of Napier, if I would come over to Acton and give them some advice on the high compression racing Lion engines they were preparing for the first official, British Government, participation in the Schneider Contest at Venice that year.
The Fleet Air Arm
Authors: Slattery Matthew
Published: July 2016

To tell the story of Naval aviation from the end of the First World War to the present requires a book but, within the confines of this short article, I shall hope to trace the changing pattern of Naval aviation in this country against the background of the aircraft which were developed and used, the carriers, the catapults and the miscellany of equipment. I shall omit the technical details of the aircraft themselves, because to include them would add greatly to the length and the details are, in any case, available in the usual reference books.
Fifty Years of Military Airworthiness
Authors: Mettam H. A.
Published: July 2016

What, for that matter, is the meaning of Airworthiness? In the early years, aerodynamics and structural strength were the main preoccupations of those concerned with the safety of aircraft and their crews, and “airworthy” meant little more than that the aircraft was believed to be safe to fly. The wider range of safety requirements covered by the British Civil Airworthiness Requirements is the subject of another chaper. In the military field, the Joint Airworthiness Committee has introduced the concept of being “safe to meet the operational needs of the Service”.
British Light Aviation
Authors: Brooks P. W.
Published: July 2016

Private flying dates from the earliest days of practical aviation. Indeed, for a time, it seemed that the development of aeroplanes would run parallel to that of motor cars and that these new vehicles would emerge primarily as a more rapid and flexible means of personal transport. Although the British military authorities rather belatedly became interested in aeroplanes in 1911–12 and increasingly thereafter involved themselves in their development, up to 1914 sporting, private and exhibition flying continued as a major part of aviation.
Gliding
Authors: Wills P. A.
Published: July 2016

For the first several hundred years of the history of gliding, the design of motorless aircraft was attempted simply because these were, in the absence of any conceivable engine, the only possible devices through which the secrets of controlled flight by human beings might be discovered. In this short paper I do not propose to record any of the doings in this field. For as one of the most unexpected outcomes of the First World War, gliding was reborn in a shape which developed it as it is today, as the greatest sport of all time, involving the use of the energy stored in the atmosphere to maintain sustained flight.
British Aircraft Industry—Men and Machines
Authors: Bowyer Edward
Published: July 2016

Although the roots of the British Aircraft Industry date back to the end of the last century—to 1898, when the brothers Horace, Eustace and Oswald Short began to manufacture balloons in makeshift premises beneath the railway arches at Battersea—it was not until the First World War that the Industry was securely founded. Thus the Royal Aeronautical Society, which this month celebrates its centenary, has existed for twice as long as the Industry.
The Rocket Propulsion Establishment, Westcott
Authors: Dunning J. E. P.
Published: July 2016

In the first issue of the Journal for 1966, the Centenary Year of the Royal Aeronautical Society, an account of the history of the Rocket Propulsion Establishment, no matter how brief, may appear to some as an unwarrantable intrusion. It is in this year, 1966, that the Establishment will complete only its second decade of existence, but it may claim to have contributed to the advancement of aeronautics, in the broadest sense of this term.
Some Time-Dependent Properties of Symmetric M/G/1 Queues
Authors: Kella Offer , Zwart Bert , Boxma Onno
Published: July 2016

We consider an M/G/1 queue that is idle at time 0. The number of customers sampled at an independent exponential time is shown to have the same geometric distribution under the preemptive-resume last-in-first-out and the processor-sharing disciplines. Hence, the marginal distribution of the queue length at any time is identical for both disciplines. We then give a detailed analysis of the time until the first departure foranysymmetric queueing discipline. We characterize its distribution and show that it is insensitive to the service discipline. Finally, we study the tail behavior of this distribution.
On Finite Moments of Full Busy Periods of GI/G/c Queues
Authors: Ghahramani Saeed , Wolff Ronald W.
Published: July 2016

For a GI/G/c queue, a full busy period is an interval that begins when an arrival finds c − 1 customers in the system, and ends when, for the first time after that, a departure leaves behind c − 1 customers in the system. We present a probabilistic proof of conditions for full busy periods to have finite moments. For queues that empty, this result may be deduced from results in the literature, but our proof is much easier. For queues that do not empty, our proof still applies, and this result is new.
A Note on Branching Random Walks on Finite Sets
Authors: Mountford Thomas , Schinazi Rinaldo B.
Published: July 2016

We show that a branching random walk that is supercritical on is also supercritical, in a rather strong sense, when restricted to a large enough finite ball of This implies that the critical value of branching random walks on finite balls converges to the critical value of branching random walks on as the radius increases to infinity. Our main result also implies coexistence of an arbitrary finite number of species for an ecological model.
Optimization under the P
M
λ,τ policy of a finite dam with both continuous and jumpwise inputs
Authors: Lim Kyung Eun , Baek Jee Seon , Lee Eui Yong
Published: July 2016

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.
The finite-time ruin probability of the compound Poisson model with constant interest force
Authors: Tang Qihe
Published: July 2016

In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate ruin probability and, in particular, is uniform for all time horizons when the claim size distribution is regularly varying tailed.
A probabilistic model for the survivability of cells
Authors: Adler Ilan , Ahn Hyun-Soo , Karp Richard M. , Ross Sheldon M.
Published: July 2016

Consider n cells, of which some are target cells, and suppose that each cell has a weight. The cells are killed in a sequential manner, with each currently live cell being the next one killed with a probability proportional to its weight. We study the distribution of the number of cells that are alive at the moment when all the target cells have been killed.
An epidemic model with exposure-dependent severities
Authors: Ball Frank , Britton Tom
Published: July 2016

We consider a stochastic model for the spread of a susceptible–infective–removed (SIR) epidemic among a closed, finite population, in which there are two types of severity of infectious individuals, namely mild and severe. The type of severity depends on the amount of infectious exposure an individual receives, in that infectives are always initially mild but may become severe if additionally exposed. Large-population properties of the model are derived. In particular, a coupling argument is used to provide a rigorous branching process approximation to the early stages of an epidemic, and an embedding argument is used to derive a strong law and an associated central limit theorem for the final outcome of an epidemic in the event of a major outbreak. The basic reproduction number, which determines whether or not a major outbreak can occur given few initial infectives, depends only on parameters of the mild infectious state, whereas the final outcome in the event of a major outbreak depends also on parameters of the severe state. Moreover, the limiting final size proportions need not even be continuous in the model parameters.
A renewal-process-type expression for the moments of inverse subordinators
Authors: Lagerås Andreas Nordvall
Published: July 2016

We define an inverse subordinator as the passage times of a subordinator to increasing levels. It has previously been noted that such processes have many similarities to renewal processes. Here we present an expression for the joint moments of the increments of an inverse subordinator. This is an analogue of a result for renewal processes. The main tool is a theorem on processes which are both renewal processes and Cox processes.
Sharp reliability bounds for the ℒ-like distributions, a class in which ageing is based on Laplace transform inequalities
Authors: Hu Chin-Yuan , Lin Gwo Dong
Published: July 2016

We establish Klar's (2002) conjecture about sharp reliability bounds for life distributions in the ℒα-class in reliability theory. The key idea is to construct a set of two-point distributions whose support points satisfy a certain system of equalities and inequalities.
A Diffusion Limit for Generalized Correlated Random Walks
Authors: Gruber Urs , Schweizer Martin
Published: July 2016

A generalized correlated random walk is a process of partial sums such that (X, Y) forms a Markov chain. For a sequence (X

n
) of such processes in which each takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly described in terms of the limiting behaviour of the transition probabilities for the Y

n
. Applications include asymptotics of option replication under transaction costs and approximation of a given diffusion by regular recombining binomial trees.
Monte Carlo Algorithms for Finding the Maximum of a Random Walk with Negative Drift
Authors: Baringhaus Ludwig , Grübel Rudolf
Published: July 2016

We discuss two Monte Carlo algorithms for finding the global maximum of a simple random walk with negative drift. This problem can be used to connect the analysis of random input Monte Carlo algorithms with ideas and principles from mathematical statistics.
A Forward Algorithm for Solving Optimal Stopping Problems
Authors: Irle Albrecht
Published: July 2016

We consider the optimal stopping problem for g(Z

n
), where Z

n
, n = 1, 2, …, is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B
0 ⊇ B
1 ⊇ B
2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection F of these sets is an optimal stopping time. Various applications are given.
A Compound Poisson Approximation Inequality
Authors: Peköz Erol A.
Published: July 2016

We give conditions under which the number of events which occur in a sequence ofm-dependent events is stochastically smaller than a suitably defined compound Poisson random variable. The results are applied to counts of sequence pattern appearances and to system reliability. We also provide a numerical example.
A monotonicity in reversible Markov chains
Authors: Lund Robert , Zhao Ying , Kiessler Peter C.
Published: July 2016

In this paper we identify a monotonicity in all countable-state-space reversible Markov chains and examine several consequences of this structure. In particular, we show that the return times toeverystate in a reversible chain have a decreasing hazard rate on the subsequence of even times. This monotonicity is used to develop geometric convergence rate bounds for time-reversible Markov chains. Results relating the radius of convergence of the probability generating function of first return times to the chain's rate of convergence are presented. An effort is made to keep the exposition rudimentary.
Monotone utility convergence
Authors: Ankirchner Stefan
Published: July 2016

We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let be a sequence of increasing filtrations converging to , and let u

n
(x) and u
∞(x) be the maximal expected utilities when investing in a financial market according to strategies adapted to and , respectively. We give sufficient conditions for the convergence u

n
(x) → u
∞(x) as n → ∞. We provide examples in which convergence does not hold. Then we consider the respective utility-based prices, π
n
and π∞, of contingent claims under (G

t

n
) and (G

t

∞). We analyse to what extent π
n
→ π∞ as n → ∞.
Dependence ordering for Markov processes on partially ordered spaces
Authors: Daduna Hans , Szekli Ryszard
Published: July 2016

We compare dependence in stochastically monotone Markov processes with partially ordered Polish state spaces using the concordance and supermodular orders. We show necessary and sufficient conditions for the concordance order to hold both in terms of the one-step transition probabilities for discrete-time processes and in terms of the corresponding infinitesimal generators for continuous-time processes. We give examples showing that a stochastic monotonicity assumption is not necessary for such orderings. We indicate relations between dependence orderings and, variously, the asymptotic variance-reduction effect in Monte Carlo Markov chains, Cheeger constants, and positive dependence for Markov processes.
Searching for searchers
Authors: Mallows Colin L. , Meloche Jean
Published: July 2016

We describe a search problem that has arisen in the context of network monitoring. Abstractly, a known (very large) region may contain one or more ‘agents’. Starting with just one agent, we search until another agent is found; this new agent can assist in the remaining search, and so on recursively.
On the asymptotic distribution of the discrete scan statistic
Authors: Boutsikas Michael V. , Koutras Markos V.
Published: July 2016

The discrete scan statistic in a binary (0-1) sequence of n trials is defined as the maximum number of successes within any k consecutive trials (n and k, n ≥ k, being two positive integers). It has been used in many areas of science (quality control, molecular biology, psychology, etc.) to test the null hypothesis of uniformity against a clustering alternative. In this article we provide a compound Poisson approximation and subsequently use it to establish asymptotic results for the distribution of the discrete scan statistic as n, k → ∞ and the success probability of the trials is kept fixed. An extreme value theorem is also provided for the celebrated Erdős-Rényi statistic.
Navigation in small-world networks: a scale-free continuum model
Authors: Franceschetti Massimo , Meester Ronald
Published: July 2016

The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to be pervasive both in nature and in engineering systems like the World Wide Web. Work of Jon Kleinberg has shown that people, using only local information, are very effective at finding short paths in a network of social contacts. In this paper we argue that the underlying key to finding short paths is scale invariance. In order to appreciate scale invariance we suggest a continuum setting, since true scale invariance happens at all scales, something which cannot be observed in a discrete model. We introduce a random-connection model that is related to continuum percolation, and we prove the existence of a unique scale-free model, among a large class of models, that allows the construction, with high probability, of short paths between pairs of points separated by any distance.
On Two Damage Accumulation Models and Their Size Effects
Authors: Ballani F. , Stoyan D. , Wolf S.
Published: July 2016

Two cumulative damage models are considered, the inverse gamma process and a composed gamma process. They can be seen as ‘continuous’ analogues of Poisson and compound Poisson processes, respectively. For these models the first passage time distribution functions are derived. Inhomogeneous versions of these processes lead to models closely related to the Weibull failure model. All models show interesting size effects.
A Lévy Process whose Jumps are Dragged by a Spherical Dynamical System
Authors: Franke Brice
Published: July 2016

We investigate the large scale behaviour of a Lévy process whose jump magnitude follows a stable law with spherically inhomogenous scaling coefficients. Furthermore, the jumps are dragged in the spherical direction by a dynamical system which has an attractor.
Voter Model and Biased Voter Model in Heterogeneous Environments
Authors: Lanchier N. , Neuhauser C.
Published: July 2016

With the rapid adoption of transgenic crops, gene flow from transgenic crops to wild relatives through pollen dispersal is of significant concern and warrants both empirical and theoretical studies to assess the risk of introduction of transgenes into wild populations. We propose to use the (biased) voter model in a heterogeneous environment to investigate the effects of recurrent gene flow from transgenic crop to wild relatives. The model is defined on the d-dimensional integer lattice that is divided into two parts, Δ and Z

d
\ Δ. Individuals carrying the transgene and individuals carrying the wild type gene compete according to the evolution rules of a (biased) voter model on Z

d
\ Δ, while the process is conditioned to have only individuals carrying the transgene on Δ. Our main findings suggest that unless transgenes confer increased fitness in wild relatives, introgression of transgenes into populations of wild plants is slow and may even be reversible without intervention. Our study also addresses the effects of different spatial planting patterns of transgenic crops on the rate of introgression.
Integration by Parts for Point Processes and Monte Carlo Estimation
Authors: Privault Nicolas , Wei Xiao
Published: July 2016

We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation with respect to the Lebesgue measure via a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard kernel estimators. This applies to random variables whose densities are not analytically known and requires the knowledge of the point process jump times.
The Downtime Distribution After a Failure of a System with Multistate Independent Components
Authors: Pievatolo Antonio
Published: July 2016

Aven and Jensen (1999) proposed an approximation to the downtime distribution for arbitrary coherent systems with binary and independent repairable components, where each component follows an alternating renewal process. The approximation is based on a mixture of the duration distributions of the cut sets in the system. We extend this approach to coherent systems composed by multistate independent components, where every component follows a semi-Markov process and where we introduce the concept of a minimal cut set in the multistate setting. We test our proposal on a simple power demand-generation system, by comparing the analytic approximation with simulation results, and we find it is accurate when the system is highly available.
Optimal Buy/Sell Rules for Correlated Random Walks
Authors: Allaart Pieter , Monticino Michael
Published: July 2016

Correlated random walks provide an elementary model for processes that exhibit directional reinforcement behavior. This paper develops optimal multiple stopping strategies - buy/sell rules - for correlated random walks. The work extends previous results given in Allaart and Monticino (2001) by considering random step sizes and allowing possibly negative reinforcement of the walk's current direction. The optimal strategies fall into two general classes - cases where conservative buy-and-hold type strategies are optimal and cases for which it is optimal to follow aggressive trading strategies of successively buying and selling the commodity depending on whether the price goes up or down. Simulation examples are given based on a stock index fund to illustrate the variation in return possible using the theoretically optimal stop rules compared to simpler buy-and-hold strategies.
Reduced Branching Processes with Very Heavy Tails
Authors: Lagerås Andreas N. , Sagitov Serik
Published: July 2016

The reduced Markov branching process is a stochastic model for the genealogy of an unstructured biological population. Its limit behavior in the critical case is well studied for the Zolotarev-Slack regularity parameter α ∈ (0, 1]. We turn to the case of very heavy-tailed reproduction distribution α = 0 assuming that Zubkov's regularity condition holds with parameter β ∈ (0, ∞). Our main result gives a new asymptotic pattern for the reduced branching process conditioned on nonextinction during a long time interval.
On the Truncated Long-Range Percolation on Z 2
Authors: de Lima Bernardo Nunes Borges , Sapozhnikov Artëm
Published: July 2016

We consider an independent long-range bond percolation onZ2. Horizontal and vertical bonds of lengthnare independently open with probabilityp_n ∈ [0, 1]. Given ∑n=1∞∏i=1n(1 −pi) < ∞, we prove that there exists an infinite cluster of open bonds of length less than or equal toNfor some large but finiteN. The result gives a partial answer to the truncation problem.
Bias and Overtaking Optimality for Continuous-Time Jump Markov Decision Processes in Polish Spaces
Authors: Zhu Quanxin , Prieto-Rumeau Tomás
Published: July 2016

In this paper we study the bias and the overtaking optimality criteria for continuous-time jump Markov decision processes in general state and action spaces. The corresponding transition rates are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. Under appropriate hypotheses, we prove the existence of solutions to the bias optimality equations, the existence of bias optimal policies, and an equivalence relation between bias and overtaking optimality.
The SIS Great Circle Epidemic Model
Authors: Neal Peter
Published: July 2016

We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.