Tricritical-like behavior of the nonlinear optical refraction at the nematic-isotropic transition in the E7 thermotropic liquid crystal

We use Z-scan technique to investigate the nonlinear optical response of the thermotropic liquid crystal E7 in the neighborhood of the nematic-isotropic phase transition. The analysis of the data for the nonlinear optical birefringence is compatible with an effective critical exponent of the order parameter, beta = 0.28 +/- 0.03, which is close to the classical value, beta = 0.25, for a tricritical point. The nonlinear optical absorption in the nematic range depends on the geometrical configuration of the nematic director with respect to the polarization beam, and vanishes in the isotropic phase.

Self-organized criticality in MHD driven plasma edge turbulence

We analyze long-range time correlations and self-similar characteristics of the electrostatic turbulence at the plasma edge and scrape-off layer in the Tokamak Chauffage Alfven Bresillien (TCABR), with low and high Magnetohydrodynamics (MHD) activity. We find evidence of self-organized criticality (SOC), mainly in the region near the tokamak limiter. Comparative analyses of data before and during the MHD activity reveals that during the high mHD activity the Hurst parameter decreases. Finally, we present a cellular automaton whose parameters are adjusted to simulate the analyzed turbulence SOC change with the MHD activity variation. (C) 2011 Published by Elsevier B.V.

Bose glass and Mott glass of quasiparticles in a doped quantum magnet

The low-temperature states of bosonic fluids exhibit fundamental quantum effects at the macroscopic scale: the best-known examples are Bose-Einstein condensation and superfluidity, which have been tested experimentally in a variety of different systems. When bosons interact, disorder can destroy condensation, leading to a 'Bose glass'. This phase has been very elusive in experiments owing to the absence of any broken symmetry and to the simultaneous absence of a finite energy gap in the spectrum. Here we report the observation of a Bose glass of field-induced magnetic quasiparticles in a doped quantum magnet (bromine-doped dichloro-tetrakis-thiourea-nickel, DTN). The physics of DTN in a magnetic field is equivalent to that of a lattice gas of bosons in the grand canonical ensemble; bromine doping introduces disorder into the hopping and interaction strength of the bosons, leading to their localization into a Bose glass down to zero field, where it becomes an incompressible Mott glass. The transition from the Bose glass (corresponding to a gapless spin liquid) to the Bose-Einstein condensate (corresponding to a magnetically ordered phase) is marked by a universal exponent that governs the scaling of the critical temperature with the applied field, in excellent agreement with theoretical predictions. Our study represents a quantitative experimental account of the universal features of disordered bosons in the grand canonical ensemble.

Ward identities in Lifshitz-like field theories

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z = 2 in six spatial dimensions.

Chaotic encryption method based on life-like cellular automata

A chaotic encryption algorithm is proposed based on the "Life-like" cellular automata (CA), which acts as a pseudo-random generator (PRNG). The paper main focus is to use chaos theory to cryptography. Thus, CA was explored to look for this "chaos" property. This way, the manuscript is more concerning on tests like: Lyapunov exponent, Entropy and Hamming distance to measure the chaos in CA, as well as statistic analysis like DIEHARD and ENT suites. Our results achieved higher randomness quality than others ciphers in literature. These results reinforce the supposition of a strong relationship between chaos and the randomness quality. Thus, the "chaos" property of CA is a good reason to be employed in cryptography, furthermore, for its simplicity, low cost of implementation and respectable encryption power. (C) 2012 Elsevier Ltd. All rights reserved.

The phenotype of Floating-Harbor syndrome: clinical characterization of 52 individuals with mutations in exon 34 of SRCAP

Background Floating-Harbor syndrome (FHS) is a rare condition characterized by short stature, delays in expressive language, and a distinctive facial appearance. Recently, heterozygous truncating mutations in SRCAP were determined to be disease-causing. With the availability of a DNA based confirmatory test, we set forth to define the clinical features of this syndrome. Methods and results Clinical information on fifty-two individuals with SRCAP mutations was collected using standardized questionnaires. Twenty-four males and twenty-eight females were studied with ages ranging from 2 to 52 years. The facial phenotype and expressive language impairments were defining features within the group. Height measurements were typically between minus two and minus four standard deviations, with occipitofrontal circumferences usually within the average range. Thirty-three of the subjects (63%) had at least one major anomaly requiring medical intervention. We did not observe any specific phenotype-genotype correlations. Conclusions This large cohort of individuals with molecularly confirmed FHS has allowed us to better delineate the clinical features of this rare but classic genetic syndrome, thereby facilitating the development of management protocols.

Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.

Indagine delle proprietà statistiche di serie temporali di posizione applicata al caso della stazione permanente GPS della base Mario Zucchelli in Terra Vittoria (Antartide)

Da ormai sette anni la stazione permanente GPS di Baia Terranova acquisisce dati giornalieri che opportunamente elaborati consentono di contribuire alla comprensione della dinamica antartica e a verificare se modelli globali di natura geofisica siano aderenti all’area di interesse della stazione GPS permanente. Da ricerche bibliografiche condotte si è dedotto che una serie GPS presenta molteplici possibili perturbazioni principalmente dovute a errori nella modellizzazione di alcuni dati ancillari necessari al processamento. Non solo, da alcune analisi svolte, è emerso come tali serie temporali ricavate da rilievi geodetici, siano afflitte da differenti tipologie di rumore che possono alterare, se non opportunamente considerate, i parametri di interesse per le interpretazioni geofisiche del dato. Il lavoro di tesi consiste nel comprendere in che misura tali errori, possano incidere sui parametri dinamici che caratterizzano il moto della stazione permanente, facendo particolare riferimento alla velocità del punto sul quale la stazione è installata e sugli eventuali segnali periodici che possono essere individuati.

Analisi della rugosità della superficie di rottura di materiali policristallini. An analysis on crack surface roughness in polycrystals

La tesi tratta l'analisi della rugosità della superficie di frattura di un materiale policristallino portato a rottura secondo il modo I. Il continuo viene discretizzato con la tassellazione di Voronoi e la duale triangolazione di Delaunay, da cui si ottiene un traliccio equivalente ovvero il modello del problema. Viene poi effettuata un'analisi elastica incrementale che porta, ad ogni passo, al raggiungimento della soglia di rottura per un elemento del traliccio, delineando così il profilo di rottura. La rugosità del profilo di rottura viene stimata attraverso il calcolo dell'esponente di Hurst, ottenuto dallo studio della funzione di correlazione delle altezze.

Sulla progettazione in zona sismica di strutture dotate di dissipatori fluido-viscosi: proposta di una metodologia

CHAPTER 1:FLUID-VISCOUS DAMPERS In this chapter the fluid-viscous dampers are introduced. The first section is focused on the technical characteristics of these devices, their mechanical behavior and the latest evolution of the technology whose they are equipped. In the second section we report the definitions and the guide lines about the design of these devices included in some international codes. In the third section the results of some experimental tests carried out by some authors on the response of these devices to external forces are discussed. On this purpose we report some technical schedules that are usually enclosed to the devices now available on the international market. In the third section we show also some analytic models proposed by various authors, which are able to describe efficiently the physical behavior of the fluid-viscous dampers. In the last section we propose some cases of application of these devices on existing structures and on new-construction structures. We show also some cases in which these devices have been revealed good for aims that lies outside the reduction of seismic actions on the structures. CHAPTER 2:DESIGN METHODS PROPOSED IN LITERATURE In this chapter the more widespread design methods proposed in literature for structures equipped by fluid-viscous dampers are introduced. In the first part the response of sdf systems in the case of harmonic external force is studied, in the last part the response in the case of random external force is discussed. In the first section the equations of motion in the case of an elastic-linear sdf system equipped with a non-linear fluid-viscous damper undergoing a harmonic force are introduced. This differential problem is analytically quite complex and it’s not possible to be solved in a closed form. Therefore some authors have proposed approximate solution methods. The more widespread methods are based on equivalence principles between a non-linear device and an equivalent linear one. Operating in this way it is possible to define an equivalent damping ratio and the problem becomes linear; the solution of the equivalent problem is well-known. In the following section two techniques of linearization, proposed by some authors in literature, are described: the first technique is based on the equivalence of the energy dissipated by the two devices and the second one is based on the equivalence of power consumption. After that we compare these two techniques by studying the response of a sdf system undergoing a harmonic force. By introducing the equivalent damping ratio we can write the equation of motion of the non-linear differential problem in an implicit form, by dividing, as usual, for the mass of the system. In this way, we get a reduction of the number of variables, by introducing the natural frequency of the system. The equation of motion written in this form has two important properties: the response is linear dependent on the amplitude of the external force and the response is dependent on the ratio of the frequency of the external harmonic force and the natural frequency of the system only, and not on their single values. All these considerations, in the last section, are extended to the case of a random external force. CHAPTER 3: DESIGN METHOD PROPOSED In this chapter the theoretical basis of the design method proposed are introduced. The need to propose a new design method for structures equipped with fluid-viscous dampers arises from the observation that the methods reported in literature are always iterative, because the response affects some parameters included in the equation of motion (such as the equivalent damping ratio). In the first section the dimensionless parameterε is introduced. This parameter has been obtained from the definition of equivalent damping ratio. The implicit form of the equation of motion is written by introducing the parameter ε, instead of the equivalent damping ratio. This new implicit equation of motions has not any terms affected by the response, so that once ε is known the response can be evaluated directly. In the second section it is discussed how the parameter ε affects some characteristics of the response: drift, velocity and base shear. All the results described till this point have been obtained by keeping the non-linearity of the behavior of the dampers. In order to get a linear formulation of the problem, that is possible to solve by using the well-known methods of the dynamics of structures, as we did before for the iterative methods by introducing the equivalent damping ratio, it is shown how the equivalent damping ratio can be evaluated from knowing the value of ε. Operating in this way, once the parameter ε is known, it is quite easy to estimate the equivalent damping ratio and to proceed with a classic linear analysis. In the last section it is shown how the parameter ε could be taken as reference for the evaluation of the convenience of using non-linear dampers instead of linear ones on the basis of the type of external force and the characteristics of the system. CHAPTER 4: MULTI-DEGREE OF FREEDOM SYSTEMS In this chapter the design methods of a elastic-linear mdf system equipped with non-linear fluidviscous dampers are introduced. It has already been shown that, in the sdf systems, the response of the structure can be evaluated through the estimation of the equivalent damping ratio (ξsd) assuming the behavior of the structure elastic-linear. We would to mention that some adjusting coefficients, to be applied to the equivalent damping ratio in order to consider the actual behavior of the structure (that is non-linear), have already been proposed in literature; such coefficients are usually expressed in terms of ductility, but their treatment is over the aims of this thesis and we does not go into further. The method usually proposed in literature is based on energy equivalence: even though this procedure has solid theoretical basis, it must necessary include some iterative process, because the expression of the equivalent damping ratio contains a term of the response. This procedure has been introduced primarily by Ramirez, Constantinou et al. in 2000. This procedure is reported in the first section and it is defined “Iterative Method”. Following the guide lines about sdf systems reported in the previous chapters, it is introduced a procedure for the assessment of the parameter ε in the case of mdf systems. Operating in this way the evaluation of the equivalent damping ratio (ξsd) can be done directly without implementing iterative processes. This procedure is defined “Direct Method” and it is reported in the second section. In the third section the two methods are analyzed by studying 4 cases of two moment-resisting steel frames undergoing real accelerogramms: the response of the system calculated by using the two methods is compared with the numerical response obtained from the software called SAP2000-NL, CSI product. In the last section a procedure to create spectra of the equivalent damping ratio, affected by the parameter ε and the natural period of the system for a fixed value of exponent α, starting from the elasticresponse spectra provided by any international code, is introduced.

L'effetto della pressione sulle perdite in condotte con fessure longitudinali - The effect of pressure on leakage in longitudinally crecked pressurized pipes.

La crescente attenzione verso un utilizzo attento, sostenibile ed economicamente efficiente della risorsa idrica rende di primaria importanza il tema delle perdite idriche e della gestione efficiente dei sistemi idrici. La richiesta di controlli dell’uso dell’acqua è stata avanzata a livello mondiale. Il problema delle perdite idriche nei Paesi industrializzati è stato così affrontato con specifiche normative e procedure di best practice gestionale per avanzare una valutazione delle perdite idriche e una limitazione degli sprechi e degli usi impropri. In quest’ambito, la pressione gioca un ruolo fondamentale nella regolazione delle perdite reali. La regolazione delle pressioni nelle diverse ore del giorno consente, infatti, di poter agire su queste ultime perdite, che aumentano all’aumentare della pressione secondo una cosiddetta legge di potenza. La motivazione della presente tesi è originata dalla necessità di quantificare il livello di perdita idrica in un sistema acquedottistico in relazione alla pressione all’interno del sistema stesso. Per avere una stima realistica che vada al di là della legge della foronomia, si vuole valutare l’influenza della deformabilità della condotta in pressione fessurata sull’entità delle perdite idriche, con particolare attenzione alle fessurazioni di tipo longitudinale. Tale studio è condotto tramite l’introduzione di un semplice modello di trave alla Winkler grazie al quale, attraverso un’analisi elastica, si descrive il comportamento di una generica condotta fessurata longitudinalmente e si valuta la quantità d’acqua perduta. I risultati ottenuti in condizioni specifiche della condotta (tipo di materiale, caratteristiche geometriche dei tubi e delle fessure, etc.) e mediante l’inserimento di opportuni parametri nel modello, calibrati sui risultati forniti da una raffinata modellazione tridimensionale agli elementi finiti delle medesime condotte, verranno poi confrontati con i risultati di alcune campagne sperimentali. Gli obiettivi del presente lavoro sono, quindi, la descrizione e la valutazione del modello di trave introdotto, per stabilire se esso, nonostante la sua semplicità, sia effettivamente in grado di riprodurre, in maniera realistica, la situazione che si potrebbe verificare nel caso di tubo fessurato longitudinalmente e di fornire risultati attendibili per lo studio delle perdite idriche. Nella prima parte verrà approfondito il problema della perdite idriche. Nella seconda parte si illustrerà il semplice modello di trave su suolo elastico adottato per l’analisi delle condotte in pressione fessurate, dopo alcuni cenni teorici ai quali si è fatto riferimento per la realizzazione del modello stesso. Successivamente, nella terza parte, si procederà alla calibrazione del modello, tramite il confronto con i risultati forniti da un’analisi tridimensionale agli elementi finiti. Infine nella quarta parte verrà ricavata la relazione flusso-pressione con particolare attenzione all’esponente di perdita, il cui valore risulterà superiore a quello predetto dalla teoria della foronomia, e verrà verificata l’effettiva validità del modello tramite un confronto con i risultati sperimentali di cui è stata fatta menzione in precedenza.

Schichtpräparation und Charakterisierung von Wellenleitern aus Polymeren

In der vorliegenden Arbeit wurde die Bedeutung verschiedener Präparationsparameter auf die Schichtpräparation von Polymerfilmen durch Schleuderbeschichtung untersucht. Insbesondere war der Einfluß der Konzentration bzw. Viskosität der Polymerlösungen, der Umdrehungszahl und der Präparationstemperatur auf die Schichtdicke und Schichtrauhigkeit von Interesse. Eine systematische Variation der Präparationsparameter wurde an Polystyrol/Toluol-, Polycarbonat/DMF- und Polycarbonat/Cyclohexanon-Lösungen vorgenommen. Es stellte sich heraus, daß eine Schichtpräparation beim Gebrauch des Lösungsmittels DMF erst bei Temperaturen oberhalb der Raumtemperatur möglich wurde. Das Auftreten von Defekten in den aus höherkonzentrierten Lösungen hergestellten Schichten ist möglicherweise auf die Bildung von Gelpartikeln in den Lösungen zurückzuführen. Die Lösungsmittelauswahl spielt daher eine Schlüsselrolle bei der Präparation defektfreier Schichten. Es sollte ein Lösungsmittel verwendet werden, dessen Löslichkeitsparameter mit dem zu lösenden Polymeren idealerweise übereinstimmt und das einen hohen Siedepunkt besitzt. Falls die Schichtdicke auf einen bestimmten Wert festgelegt ist, so folgen aus den Polystyrol- und Polycarbonatergebnissen unterschiedliche Schlußfolgerungen zur Reduzierung der Rauhigkeit, die sich jedoch auf einen gemeinsamen Nenner bringen lassen. Betrachtet man die an Polystyrol- und Polycarbonatschichten gewonnenen Resultate gemeinsam, so erscheint es zur Reduzierung der Rauhigkeit bei vorgegebener Schichtdicke sinnvoller, die Präparation bei großer Umdrehungszahl und hoher Konzentration durchzuführen als bei kleiner Umdrehungszahl aus niederkonzentrierten Lösungen. Eine Variation der Präparationstemperatur erweist sich als außerordentlich hilfreich zur Optimierung der Schichtqualität. Dies zeigt sich insbesondere bei der Präparation von Polycarbonat-, D/A-PPV- und Polyvinylkarbazol-Schichten, wenn DMF als Lösungsmittel verwendet wird. Durch eine Temperaturerhöhung ist zudem eine größere Schichtdicke erreichbar. Dies kann sich unter Umständen bei schwerlöslichen Substanzen als vorteilhaft erweisen, um die für Wellenleiteranwendungen erforderliche Mindestschichtdicke zu erreichen. Aus den Abhängigkeiten der Schichtdicke von den Präparationsparametern Konzentration und Umdrehungszahl lassen dich Potenzgesetze der Form ? ableiten. Der Exponent ? hängt vom speziellen Polymer/Lösungsmittelsystem und von der Temperatur ab; für ? wurde meistens ein Wert von -0.5 gefunden. Zur Bestimmung der Exponenten sind nur vier verschiedene Parametersätze (?,?) notwendig. Bei Kenntnis von ? und ? kann die Schichtdicke für eine beliebige (?,?)-Kombination im voraus in guter Näherung bestimmt werden, was in der Praxis häufig nützlich ist. Durch Beachtung dieser Präparationsregeln konnten neben dämpfungsarmen Polystyrol- und Polycarbonatschichten auch filme aus konjugierten Polymeren hergestellt werden, deren Dämpfungskoeffizienten teilweise deutlich unter 1 dB/cm lagen. Hier sind besonders die Resultate an DPOP-PPV und CNE-PPV Schichten hervorzuheben. Die erreichten Dämpfungswerte sind besser bzw. vergleichbar mit den geringsten Werten, die bisher in der Literatur zu konjugierten Polymerfilmen veröffentlicht wurden. Bei einigen Substanzen scheiterte die Präparation ausreichend dicker Filme bzw. Dämpfungsmessungen an einer zu geringen Löslichkeit oder an der Bildung polykristalliner Domänen bzw. sonstiger Defekte. Dies macht deutlich, daß eine erfolgreiche Schichtpräparation wesentlich von der chemischen struktur abhängt. Die Abschätzung des Güteparameters (Figure Of Merit) ergab mit den gemessenen nichtlinear-optischen Suszeptibilitäten ?

Monte Carlo-Simulationen zum kritischen Verhalten dünner Ising-Filme

Monte Carlo-Simulationen zum kritischen Verhalten dünnerIsing-Filme Dünne Ising-Filme können als vereinfachtes Modell zurBeschreibung von binären Mischungen oder von Flüssigkeitenin schlitzartigen Kapillaren dienen. Infolge dereingeschränkten Geometrie unterscheidet sich das kritischeVerhalten dieser Systeme signifikant von dem einesBulk-Systems, es kommt zu einem Crossover von zwei- zudreidimensionalem kritischen Verhalten. Zusätzlichverschiebt sich der Phasenübergang in den ungesättigtenBereich, ein Effekt, der als 'capillary condensation'bezeichnet wird. In der vorliegenden Arbeit wurden die kritischenEigenschaften von Ising-Filmen im Rahmen einer MonteCarlo-Simulation untersucht. Zur Verbesserung der Effizienzwurde ein Cluster-Algorithmus verwendet, der um einenGhost-Spin-Term zur Behandlung der Magnetfelder erweitertwar. Bei der Datenanalyse kamen moderneMulti-Histogramm-Techniken zur Anwendung. Für alle untersuchten Schichtdicken konnten kritischeTemperatur und Magnetfeld sehr präzise bestimmt werden. DieSkalenhypothese von Fisher und Nakanishi, die dieVerschiebung des kritischen Punktes gegenüber seinesBulk-Wertes beschreibt, wurde sowohl für Systeme mit freienOberflächen als auch für Systeme mit schwachemOberflächenfeld bestätigt. Der Wert des Gap-Exponenten derOberfläche wurde mit $Delta_1$=0.459(13) in Übereinstimmungmit den Literaturwerten abgeschätzt. Die Observablen Magnetisierung und magnetischeSuszeptibilität sowie deren auf die Oberfläche bezogenenEntsprechungen zeigen kein reines zweidimensionaleskritisches Verhalten. Zu ihrer Beschreibung in der Nähe deskritischen Punktes wurden effektive Exponenten für dieeinzelnen Schichtdicken bestimmt.

87 Rb-NMR-Untersuchungen an Trirubidiumhydrogendisulfat

In einer Vielzahl von Ionenkristallen mit Wasserstoffbrücken kann der Übergang aus einer paraelektrischen in eine elektrisch geordnete Phase mittels Substitution der Deuteronen durch Protonen um typischerweise 100 K abgesenkt werden. Die Ursache dieses Isotopieeffekts wird in Tunnelmoden der Protonen, in der Kopplung der Protonen untereinander oder in der Geometrie bzw. Symmetrie der Wasserstoffbrücke gesucht. Als Modellsubstanzen zur Untersuchung bieten sich die Trialkalihydrogendisulfate an. Hier sind die Wasserstoffbrücken, welche die Sulfattetraeder lokal zu Dimeren vernetzen, weit voneinander getrennt. Daher wird kein langreichweitiges Wasserstoffbrückennetzwerk ausgebildet.Bei den in dieser Arbeit untersuchten Rb3H1-xDx(SO4)2-Kristallen tritt der Phasenübergang im deuterierten Kristall bei 82 K auf und ist in protonierten Proben vollständig unterdrückt. Es wurde die 87Rb-NMR eingesetzt, weil damit Untersuchungen von Struktur und Dynamik im gesamten Konzentrationsbereich möglich sind. Die Meßgröße ist der elektrische Feldgradient (EFG), welcher durch die umgebenden Ionenladungen erzeugt wird.Durch orientierungsabhängige Messungen wurde gezeigt, daß die drei in der paraelektrischen Phase von Rb3D(SO4)2 vorkommenden EFG sich nicht durch Symmetrieoperationen ineinander überführen lassen. Es liegen somit kleine Abweichungen von einer monoklinen Symmetrie vor. Am Übergang in die antiferroelektrische Phase vervierfacht sich die Anzahl der kristallografisch inäquivalenten Einbaulagen. Aus dem Vergleich von NMR und Röntgenbeugung kann geschlossen werden, daß die Abweichungen von der monoklinen Raumgruppe und die elektrische Ordnung primär durch die Wasserstoffkerne verursacht werden. Aus der Aufspaltung der Resonanzlinien wurde ein statischer kritischer Exponent von  = 0,21  0,03 ermittelt, der mit trikritischem Verhalten verträglich ist. Die longitudinale Relaxation der Kernspinmagnetisierung wird durch Fluktuationen des EFG verursacht. Am Phasenübergang sind diese Fluktuationen an der Einbaulage der Rubidiumatome vergleichsweise groß und stark anisotrop. Beides läßt sich gut beschreiben, wenn angenommen wird, daß nur die Dynamik der Wasserstoffkerne die Kernspins relaxieren läßt. Für die longitudinale Relaxation wurde ebenfalls ein kritisches Verhalten am Phasenübergang gefunden. Der Exponent beträgt in deuterierten Proben  = -0,67 +- 0,07 und ist für die teildeuterierte Proben mit x = 0,5 größer:  = -1,15 +- 0,15. In der vorliegenden Arbeit konnte gezeigt werden, daß zur Beschreibung der NMR an verschiedenen Kernsorten weder, wie zuvor in der Literatur diskutiert, asymmetrische Wasserstoffbrücken noch Tunnelmoden erforderlich sind. Die hier erstmalig in den Trialkalihydrogendisulfaten gefundenen konzentrationsabhängigen kritischen Exponenten bilden einen neuen Prüfstein für die Modelle des Isotopieeffekts, die sich bisher primär auf die Erklärung der Phasenübergangstemperatur beschränkt haben.