Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations

We apply the method of multiple scales (MMS) to a well-known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the timescale of typical cutting tool oscillations. The MMS up to second order, recently developed for such systems, is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than the first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy in that plotted solutions of moderate amplitudes are visually near-indistinguishable. The advantages of the present analysis are that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space; lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS; the strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly; and though certain parameters are treated as small (or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation.

Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem for Laplace's equation which is a generalization of the one occurring in the course of solution of the problem of diffraction of surface water waves by a nearly vertical submerged barrier. The method of solution involves the use of complex function theory, the Schwarz reflection principle, and reduction to a system of two uncoupled Riemann-Hilbert problems. Known results, representing the reflection and transmission coefficients of the water wave problem involving a nearly vertical barrier, are derived in terms of the shape function.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

The problem of conserving amphibians in the Western Ghats, India

Habitat distruction and hunting for dissection specimens have taken their toll. But there may be other, subtle factors causing loss of amphibian populations.

Metsän erirakenteisuutta edistävien hakkuiden kannattavuustarkastelu metsäaluetasolla

Tutkimuksessa vertailtiin metsän erirakenteisuutta edistävien poimintahakkuiden ja pienaukkohakkuiden kannattavuutta metsänhoitosuositusten mukaiseen metsänkasvatukseen Keski-Suomessa. Poimintahakkuut ja pienaukkohakkuut ovat menetelmiä, joilla voidaan lisätä luonnonmetsän häiriödynamiikan mukaista pienipiirteistä elinympäristöjen vaihtelua ja siksi ne sopivat etenkin erityiskohteisiin monimuotoisuuden, maiseman tai metsien monikäytön vuoksi. Ne johtavat yleensä vähitellen eri-ikäisrakenteiseen metsään, jossa puuston läpimittaluokkajakauma muistuttaa käänteistä J-kirjainta. Eri-ikäisrakenteisen metsänkäsittelyn taloudellista kannattavuutta puoltavat uudistumiskustannusten poisjäänti ja tukkipuihin painottuvat säännöllisin väliajoin toteutuvat hakkuut. Menetelmän soveltumista Suomen olosuhteisiin pidetään kuitenkin epävarmana. Tässä tutkimuksessa tarkasteltiin tasaikäisrakenteisen metsän muuttamista eri-ikäisrakenteiseksi 40 vuoden siirtymäaikana Metsähallituksen hallinnoimassa Isojäven ympäristöarvometsässä Kuhmoisissa. Tutkimusaineisto koostui 405 kuusivaltaisesta tasaikäisestä kuviosta, joiden pinta-alasta metsämaata on 636 hehtaaria. Metsän kehitystä simuloitiin puutason kasvumalleja käyttäen ja käsittelytoimenpiteet simuloitiin viisivuotiskausittain SIMO-metsäsuunnitteluohjelmistolla. Simulointien avulla selvitettiin jokaisen käsittelyskenaarion hakkuumäärät puutavaralajeittain, diskontatut kassavirrat ja puustopääoman muutos tarkasteluajanjakson aikana. Puunkorjuun yksikkökustannusten laskennan apuna käytettiin automatisoitua seurantajärjestelmää, jossa metsäkoneisiin asennettuilla matkapuhelimilla kerättiin MobiDoc2-sovelluksella metsäkoneiden käytöstä kiihtyvyystiedot, GPS-paikkatiedot ja syötetiedot. Lopulta jokaiselle käsittelyskenaariolle laskettiin metsän puuntuotannollista arvoa kuvaavalla tuottoarvon yhtälöllä nettonykyarvot, josta vähennettiin diskontatut puunkorjuun kustannukset. Tutkimuksen tulosten mukaan poimintahakkuun NPV oli 3 prosentin korkokannalla noin 91 % (7420 €/ha) ja pienaukkohakkuiden noin 99 % (8076 €/ha) metsänhoitosuositusten mukaisesta käsittelystä (8176 €/ha). Komparatiivinen statiikka osoitti, että korkokannan kasvattaminen 5 prosenttiin ei olennaisesti lisännyt nettonykyarvojen eroja. Poimintahakkuiden puunkorjuun yksikkökustannukset olivat 0,8 €/m3 harvennushakkuita pienemmät ja 7,2 €/m3 uudistushakkuita suuremmat. Pienaukkohakkuiden yksikkökustannukset olivat 0,7 €/m3 uudistushakkuita suuremmat.Tulosten perusteella on väistämätöntä että siirtymävaihe tasaikäisrakenteisesta eri-ikäisrakenteiseksi metsäksi aiheuttaa taloudellisia tappioita siitäkin huolimatta, että hakkuut ovat voimakkaita ja tehdään varttuneeseen kasvatusmetsään. Tappion määrä on metsän peitteisyyden ylläpidosta aiheutuva vaihtoehtoiskustannus.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A Direct Approach to the Problem of Diffraction by a Half-Plane under Mixed Boundary Conditions

A general direct technique of solving a mixed boundary value problem in the theory of diffraction by a semi-infinite plane is presented. Taking account of the correct edge-conditions, the unique solution of the problem is derived, by means of Jones' method in the theory of Wiener-Hopf technique, in the case of incident plane wave. The solution of the half-plane problem is found out in exact form. (The far-field is derived by the method of steepest descent.) It is observed that it is not the Wiener-Hopf technique which really needs any modification but a new technique is certainly required to handle the peculiar type of coupled integral equations which the Wiener-Hopf technique leads to. Eine allgemeine direkte Technik zur Lösung eines gemischten Randwertproblems in der Theorie der Beugung an einer halbunendlichen Ebene wird vorgestellt. Unter Berücksichtigung der korrekten Eckbedingungen wird mit der Methode von Jones aus der Theorie der Wiener-Hopf-Technik die eindeutige Lösung für den Fall der einfallenden ebenen Welle hergeleitet. Die Lösung des Halbebenenproblems wird in exakter Form angegeben. (Das Fernfeld wurde mit der Methode des steilsten Abstiegs bestimmt.) Es wurde bemerkt, daß es nicht die Wiener-Hopf-Technik ist, die wirklich irgend welcher Modifikationen bedurfte. Gewiß aber wird eine neue Technik zur Behandlung des besonderen Typs gekoppelter Integralgleichungen benötigt, auf die die Wiener-Hopf-Technik führt.

Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Vehicle Routing Problem with Load Compatibility Constraints

The major contribution of this paper is to introduce load compatibility constraints in the mathematical model for the capacitated vehicle routing problem with pickup and deliveries. The employee transportation problem in the Indian call centers and transportation of hazardous materials provided the motivation for this variation. In this paper we develop a integer programming model for the vehicle routing problem with load compatibility constraints. Specifically two types of load compatability constraints are introduced, namely mutual exclusion and conditional exclusion. The model is demonstrated with an application from the employee transportation problem in the Indian call centers.

Neural network approach for the two-dimensional assignment problem

A neural network approach for solving the two-dimensional assignment problem is proposed. The design of the neural network is discussed and simulation results are presented. The neural network obtains 10-15% lower cost placements on the examples considered, than the adjacent pairwise exchange method.

A New Approach to the Problem of Scattering of Water Waves by Vertical Barriers

Using a modified Green's function technique the two well-known basic problems of scattering of surface water waves by vertical barriers are reduced to the problem of solving a pair of uncoupled integral equations involving the “jump” and “sum” of the limiting values of the velocity potential on the two sides of the barriers in each case. These integral equations are then solved, in closed form, by the aid of an integral transform technique involving a general trigonometric kernel as applicable to the problems associated with a radiation condition.