On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Introduktionen av kärnkraften i Finland

Finlands industri har av tradition varit starkt energikrävande. Träförädlingsindustrin, som fick sin egentliga start i medlet på 1800-talet, använde stora mängder energi liksom metallförädlingsföretagen i ett senare skede. Krigstiden med sin energiransonering visade handgripligen för allmänheten liksom för specialisterna att en tillräcklig tillgång till energi är ett livsvillkor för vår industri och därmed för vårt land. Efterkrigstiden kännetecknades av en allt snabbare utbyggnad av den på vatten- och ångkraft baserade elkraftskapaciteten, en utbyggnad som den inhemska verkstadsindustrin i stor utsträckning deltog i. Men redan på 1950-talet var vattenkraften till stor del utbyggd, varför den privata såväl som den statliga sektorns intresse allt mera inriktade sig på den speciellt i USA favoriserade atomenergin. Efter fördjupade studier i kärnfysik och kärnteknik vid the International School of Nuclear Science and Engineering i USA deltog författaren av dessa rader intensivt (först som Ahlströmanställd och senare som VD för Finnatom) i den utvecklingsverksamhet inom det kärntekniska området som inte bara elproducenterna utan även verkstadsindustrin i vårt land genomförde. Det var därför naturligt för mig att som objekt för min doktorsavhandling välja introduktionen av kärnkraften i Finland med speciell fokus på den inhemska verkstadsindustrins roll. Jag ställde följande forskningsfrågor: a. När och hur skedde introduktionen av kärnkraften i Finland? b. Vilka var orsakerna till och resultatet av denna introduktion? c. Vilken var den inhemska verkstadsindustrins roll? Ett grundligt studium av litteraturen inklusive mötesprotokoll och tidningsreferat samt personligen genomförda intervjuer med ett trettiotal av de verkliga aktörerna i den långa och komplicerade introduktionsprocessen ledde till en teori, vars riktighet jag anser mig ha kunnat bevisa. Den inhemska verkstadsindustrins roll var synnerligen central. Dess representanter lyckades, bl.a. refererande till erfarenheterna från utbyggnaden av vatten- och ångkraften liksom till byggandet av den underkritiska milan YXP samt forskningsreaktorn TRIGA, övertyga beslutsfattarna om att den besatt nödig kompetens för att kompensera den kompetensbrist som kunde iakttas inom vissa områden hos den sovjetiska kärnkraftverksleverantören. De inhemska leveranserna påverkade även driftsresultatet, speciellt i fallet Lovisa, i positiv riktning. Introduktionsprocessen, som omfattade tiden från slutet av 1950-talet till början på 1980-talet, beskrevs, noterande bl.a. J. W. Creswells anvisningar, i detalj i avhandlingen. Introduktionen fick som resultat konkurrenskraftig elkraft, impuls till start av nya företag, exempelvis Nokia Elektronik, liksom en klar höjning av den tekniska nivån hos vår industri, inkluderande kärnteknisk tillverkning i stor skala. Katastrofen i Tjernobyl i slutet av april 1986 innebar emellertid att utvecklingen tog en paus på ett par decennier. Erfarenheterna från introduktionsfasen kan förhoppningsvis utnyttjas till fullo nu, när utbyggnaden av kärnkraften återupptagits i vårt land.

Vibration free machining tools

Appearance of the vibration is the very important problem in long tool turning and milling. Current solutions of minimizing vibrations provided by different tool suppliers are very expensive. This Master’s Thesis is presenting the new type of vibration free machining tools produced by Konepaja ASTEX Gear Oy that have cheaper production costs compare to competitors’ products. Vibration problems in machining and their today’s solutions are analyzed in this work. The new vibration damping invention is presented and described. Moreover, the production, laboratory experimental modal analysis and practical testing of the new vibration free prototypes are observed and analyzed on the pages of this Thesis. Based on the testing results the new invention is acknowledged to be successful and approved for further studies and developments.

Teollisuusprosessien signaalien automaattinen analysointi

Diplomityössä kehitettiin menetelmiä teollisuusprosessien signaalien automaattiseen havainnointiin ja luotiin työkalu tulosten esittämiseen. Työn tarkoituksena on nopeuttaa ja helpottaa prosessin ongelmien ratkaisua luokittelemalla signaalit matemaattisten menetelmien avulla. Koska prosessin mittaussignaalit ovat pääasiassa stokastisia, eli niitä ei voida etukäteen ennustaa, käsitellään signaaleita tilastomatemaattisin keinoin. Työstä rajattiin mittaushistorian käyttö, joten värähtelyiden tunnistus toteutettiin taajuusanalyysin avulla. Korrelaation avulla löydetään samankaltaiset signaalit. Testeissä todettiin, että työssä kehitetyt havainnoinnit toimivat eri näytteenottotaajuuksilla ja työkalun suoritusnopeus todettiin hyväksi. Lopuksi esiteltiin todellinen teollisuusprosessin ongelma ja siihen mahdollisia ratkaisuja.

Memristive Computing

Memristive computing refers to the utilization of the memristor, the fourth fundamental passive circuit element, in computational tasks. The existence of the memristor was theoretically predicted in 1971 by Leon O. Chua, but experimentally validated only in 2008 by HP Labs. A memristor is essentially a nonvolatile nanoscale programmable resistor — indeed, memory resistor — whose resistance, or memristance to be precise, is changed by applying a voltage across, or current through, the device. Memristive computing is a new area of research, and many of its fundamental questions still remain open. For example, it is yet unclear which applications would benefit the most from the inherent nonlinear dynamics of memristors. In any case, these dynamics should be exploited to allow memristors to perform computation in a natural way instead of attempting to emulate existing technologies such as CMOS logic. Examples of such methods of computation presented in this thesis are memristive stateful logic operations, memristive multiplication based on the translinear principle, and the exploitation of nonlinear dynamics to construct chaotic memristive circuits. This thesis considers memristive computing at various levels of abstraction. The first part of the thesis analyses the physical properties and the current-voltage behaviour of a single device. The middle part presents memristor programming methods, and describes microcircuits for logic and analog operations. The final chapters discuss memristive computing in largescale applications. In particular, cellular neural networks, and associative memory architectures are proposed as applications that significantly benefit from memristive implementation. The work presents several new results on memristor modeling and programming, memristive logic, analog arithmetic operations on memristors, and applications of memristors. The main conclusion of this thesis is that memristive computing will be advantageous in large-scale, highly parallel mixed-mode processing architectures. This can be justified by the following two arguments. First, since processing can be performed directly within memristive memory architectures, the required circuitry, processing time, and possibly also power consumption can be reduced compared to a conventional CMOS implementation. Second, intrachip communication can be naturally implemented by a memristive crossbar structure.

Väsymiskestävyyden määritys murtumismekaanisilla särönmallinnusohjelmilla

Tässä työssä tutkitaan Wärtsilä Oyj:n moottorin ja ABB Oy:n generaattorin muodostaman aggregaatin väsymiskestävyyttä lineaarisen murtumismekaniikan avulla. Työn tavoitteena on selvittää ABAQUS/XFEM- ja FRANC3D-ohjelman soveltuvuus kuormitukseltaan ja geometrialtaan vaativan generaattorirungon suunnittelutyökaluksi. Generaattorirungon kuormitukset aiheutuvat aggregaatin käynnin sekä käynnistys- ja sammutusvaiheen aikai-sista syntyvistä värähtelyistä. Tutkimuksessa tarkastellaan generaattorirungon väsymistä käynninaikaisella kuormituksella. Työssä mallinnettiin generaattorirungosta valittu hitsausdetalji alimallinnustekniikalla, jolloin alimallin reunaehdot voitiin määrittää aggregaatille tehdyn vastelaskennan perus-teella. Alimallista tutkittiin kahta erilaista hitsiliitostyyppiä, joihin mallinnettiin XFEM- ja FRANC3D-ohjelmilla erikokoisia säröjä hitsiliitosten rajaviivalle sekä juuren puolelle. Tutkittavilla ohjelmilla saatujen jännitysintensiteettikertoimien avulla säröille voitiin las-kea ekvivalentti jännitysintensiteettikerroin, jota verrattiin kokeellisesti saatuun jännitysin-tensiteettikertoimen kynnysarvoon. XFEM- ja FRANC3D-ohjelmia vertailtiin käytön helppouden, tulosten tarkkuuden sekä laskenta-aikojen perusteella. Käytettävyyden ja laskenta-aikojen perusteella XFEM-ohjelma soveltui paremmin käytettäväksi teollisuudessa suunnittelu- ja kehitystyön apu-työkaluna. FRANC3D taas antoi XFEM-ohjelmaa luotettavampia tuloksia, mutta laskenta-ajat olivat moninkertaiset.

Multibody Simulation Model of the Roller Test Rig

Multibody simulation model of the roller test rig is presented in this work. The roller test rig consists of a paper machine’s tube roll supported with a hard bearing type balancing machine. The simulation model includes non-idealities that are measured from the physical structure. These non-idealities are the shell thickness variation of the roll and roundness errors of the shafts of the roll. These kinds of non-idealities are harmful since they can cause subharmonic resonances of the rotor system. In this case, the natural vibration mode of the rotor is excited when the rotation speed is a fraction of the natural frequency of the system. With the simulation model, the half critical resonance is studied in detail and a sensitivity analysis is performed by simulating several analyses with slightly different input parameters. The model is verified by comparing the simulation results with those obtained by measuring the real structure. Comparison shows that good accuracy is achieved, since equivalent responses are achieved within the error limit of the input parameters.

Vesihöyrypiirin kiertolaskenta kuplapetikattilassa

Työssä selvitetään kiertolaskennan periaatteita kuplapetikattilassa, esitetään lyhyesti kattilan toimintaperiaate ja paneudutaan alan laskentaohjelmistoihin. Luonnonkierto kattilan vesihöyrypiirissä on seurausta hydrostaattisesta paineesta, joka aiheutuu tiheyserosta nousu- ja laskuputkien välillä. Kiertolaskennassa on huomioitava kaksifaasivirtauksen ominaispiirteet. Höyry ja neste virtaavat putkistossa eri nopeuksilla, jolloin esimerkiksi painehäviön määrityksessä käytetään erilaisia korrelaatioita ja käyrästöjä. Kaksifaasivirtauksen laskennassa tarvitaan kolmea eri taseyhtälöä: energiatasetta, massatasetta ja liikemäärätasetta. Luonnonkiertokattiloissa höyrykierron suunnittelussa on kaksi pääasiallista ehtoa. Ensimmäiseksi tulee varmistaa riittävä kiertoveden massavirta, jotta vältetään höyrystinputkien puhki palaminen. Toiseksi tulee välttää höyrystinputken pinnan lämpötilavaihteluita ja värähtelyitä. Alustavassa luonnonkierron mitoituksessa turvaudutaan kokemusperäiseen tietoon. Myöhemmässä tarkemmassa mitoituksessa käytettäviä ohjelmistoja ovat NOWA sekä kaupalliset PPSD ja Apros. Laskenta lähtee liikkeelle siitä, että lasketaan ensin vesihöyrykierron massavirrat erilaisilla lämpökuormilla ja höyryntuotanto määritellään painehäviöiden perusteella. NOWA- ja PPSD- ohjelmistoilla tehtyjen esimerkkilaskelmien perusteella voidaan sanoa, että tulokset riippuvat käytetystä laskentamallista.

Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines

An analytical study of the nonlinear vibrations of a multiple machines portal frame foundation is presented. Two unbalanced rotating machines are considered, none of them resonant with the lower natural frequencies of the supporting structure. Their combined frequencies is set in such a way as to excite, due to nonlinear behavior of the frame, either the first anti-symmetrical mode (sway) or the first symmetrical mode. The physical and geometrical characteristics of the frame are chosen to tune the natural frequencies of these two modes into a 1:2 internal resonance. The problem is reduced to a two degrees of freedom model and its nonlinear equations of motions are derived via a Lagrangian approach. Asymptotic perturbation solutions of these equations are obtained via the Multiple Scales Method.

Accuracy of modelling and identification of malfunctions in rotor systems: experimental results

The accuracy of modelling of rotor systems composed of rotors, oil film bearings and a flexible foundation, is evaluated and discussed in this paper. The model validation of different models has been done by comparing experimental results with numerical results by means. The experimental data have been obtained with a fully instrumented four oil film bearing, two shafts test rig. The fault models are then used in the frame of a model based malfunction identification procedure, based on a least square fitting approach applied in the frequency domain. The capability of distinguishing different malfunctions has been investigated, even if they can create similar effects (such as unbalance, rotor bow, coupling misalignment and others) from shaft vibrations measured in correspondence of the bearings.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Onset of Nucleate Boiling and Onset of Fully Developed Subcooled Boiling Using Pressure Transducers Signals Spectral Analysis

The experimental technique used for detection of subcooled boiling through analysis of the fluctuation contained in pressure transducer signals is presented. This work was partly conducted at the Institut für Kerntechnik und zertörungsfreie Prüfverfahren von Hannover (IKPH, Germany) in a thermal-hydraulic circuit with one electrically heated rod with annular geometry test section. Piezoresistive pressure sensors are used for onset of nucleate boiling (ONB) and onset of fully developed boiling (OFDB) detection using spectral analysis/ signal correlation techniques. Experimental results are interpreted by phenomenological analysis of these two points and compared with existing correlation. The results allow us to conclude that this technique is adequate for the detection and monitoring of the ONB and OFDB.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.