scispace - formally typeset
Search or ask a question

Showing papers by "Chalmers University of Technology published in 1996"


Journal ArticleDOI
TL;DR: The article consists of background material and of the basic problem formulation, and introduces spectral-based algorithmic solutions to the signal parameter estimation problem and contrast these suboptimal solutions to parametric methods.
Abstract: The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

4,410 citations


Journal ArticleDOI
TL;DR: In this article, a general classification of two-phase flows and a number of possible ways to formulate two-fluid models are discussed, and a general procedure to develop such a model is presented.

522 citations


Journal ArticleDOI
TL;DR: Bringing together 44 landmark papers, "Optical Angular Momentum" offers the first comprehensive overview of the subject as it has developed and gives a definitive statement of the current status of all aspects of optical angular momentum.
Abstract: Spin angular momentum of photons and the associated polarization of light has been known for many years. However, it is only over the last decade or so that physically realizable laboratory light beams have been used to study the orbital angular momentum of light. In many respects, orbital and spin angular momentum behave in a similar manner, but they differ significantly in others. In particular, orbital angular momentum offers exciting new possibilities with respect to the optical manipulation of matter and to the study of the entanglement of photons.Bringing together 44 landmark papers, "Optical Angular Momentum" offers the first comprehensive overview of the subject as it has developed. It chronicles the first decade of this important subject and gives a definitive statement of the current status of all aspects of optical angular momentum. In each chapter, the editors include a concise introduction, putting the selected papers into context and outlining the key articles a

489 citations


Journal ArticleDOI
TL;DR: The force between atoms, molecules, clusters, complexes, surfaces, and other fragments of matter is dominated by the weak but long-ranged van der Waals interactions at large separations and general formulas have been derived for the interaction between solid bodies.
Abstract: The history of van der Waals or dispersion forces dates a long way back [1, 2]. The recent book Van der Waals and Molecular Sciences [1] gives a detailed account of van der Waals’s own contributions and life-long interest in the field. It is interesting to note that this truly quantum-mechanical problem [3, 4, 5] has been addressed by theorists long before the birth of quantum mechanics. The force between atoms, molecules, clusters, complexes, surfaces, and other fragments of matter is dominated by the weak but long-ranged van der Waals interactions at large separations. This is the region that has been primarily addressed. Calculations of the interaction potential between neutral species were first done for molecules [6, 7], leading to the well known asymptotic R −6 form of London [5]. The asymptotic z −3 form of the interaction potential between a neutral atom and a surface was first identified by Lennard-Jones [8], with subsequent refined treatments of the atom and surface polarizabilities [9, 10]. For the interaction between solid bodies, general formulas have been derived [11], which for flat surfaces a long distance d apart give an interaction energy that varies as d −2 [12]. For very large distances, where the limited magnitude of the velocity of light matters, retardation effects are important [13]. Such relativistic effects are physically interesting but beyond the scope of the present work.

433 citations


Journal ArticleDOI
TL;DR: In this article, conformal mapping-based models for interdigital capacitors on substrates with a thin superstrate and/or covering dielectric film are given for ICs with finger numbers n/spl ges/2.
Abstract: Conformal mapping-based models are given for interdigital capacitors on substrates with a thin superstrate and/or covering dielectric film. The models are useful for a wide range of dielectric constants and layer thicknesses. Capacitors with finger numbers n/spl ges/2 are discussed. The finger widths and spacing between them may be different. The results are compared with the available data and some examples are given to demonstrate the potential of the models.

400 citations


Journal ArticleDOI
TL;DR: A maximum-likelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site and a signal detection technique based on the finite alphabet property that is different from a standard linear combiner are introduced.
Abstract: We propose a maximum-likelihood (ML) approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for BPSK signals. We introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful In wireless communication systems. Simulation results demonstrate its promising performance.

379 citations


Journal ArticleDOI
TL;DR: The result with the smooth (electropolished) implants indicates that a reduction of surface roughness, in the initial phase, decreases the rate of bone formation in rabbit cortical bone.

367 citations


Journal ArticleDOI
TL;DR: The lower-range values of the theoretically calculated yields of glycerol were in good agreement with the experimental yields, which may indicate that the regulation of metabolism succeeds in the most efficient balancing of the redox potential.
Abstract: To prevent the loss of raw material in ethanol production by anaerobic yeast cultures, glycerol formation has to be reduced. In theory, this may be done by providing the yeast with amino acids, since the de novo cell synthesis of amino acids from glucose and ammonia gives rise to a surplus of NADH, which has to be reoxidized by the formation of glycerol. An industrial strain of Saccharomyces cerevisiae was cultivated in batch cultures with different nitrogen sources, i.e., ammonium salt, glutamic acid, and a mixture of amino acids, with 20 g of glucose per liter as the carbon and energy source. The effects of the nitrogen source on metabolite formation, growth, and cell composition were measured. The glycerol yields obtained with glutamic acid (0.17 mol/mol of glucose) or with the mixture of amino acids (0.10 mol/mol) as a nitrogen source were clearly lower than those for ammonium-grown cultures (0.21 mol/mol). In addition, the ethanol yield increased for growth on both glutamic acid (by 9%) and the mixture of amino acids (by 14%). Glutamic acid has a large influence on the formation of products; the production of, for example, alpha-ketoglutaric acid, succinic acid, and acetic acid, increased compared with their production with the other nitrogen sources. Cultures grown on amino acids have a higher specific growth rate (0.52 h-1) than cultures of both ammonium-grown (0.45 h-1) and glutamic acid-grown (0.33 h-1) cells. Although the product yields differed, similar compositions of the cells were attained. The NADH produced in the amino acid, RNA, and extracellular metabolite syntheses was calculated together with the corresponding glycerol formation. The lower-range values of the theoretically calculated yields of glycerol were in good agreement with the experimental yields, which may indicate that the regulation of metabolism succeeds in the most efficient balancing of the redox potential.

360 citations


Proceedings ArticleDOI
01 Jan 1996
TL;DR: A type-based analysis is designed and implemented for proving some basic properties of reactive systems and an appropriate semantic model of sized types is developed to establish the soundness of the analysis.
Abstract: We have designed and implemented a type-based analysis for proving some basic properties of reactive systems. The analysis manipulates rich type expressions that contain information about the sizes of recursively defined data structures. Sized types are useful for detecting deadlocks, nontermination, and other errors in embedded programs. To establish the soundness of the analysis we have developed an appropriate semantic model of sized types.

352 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a simple model that predicts the changes in resonance frequency and dissipation factor for a quartz-crystal microbalance (QCM) when it is coated with a viscous film that may or may not slip on the crystal.
Abstract: We present a simple model that predicts the changes in resonance frequency and dissipation factor for a quartz-crystal microbalance (QCM) when it is coated with a viscous film that may or may not slip on the crystal. In this context, the validity of the Sauerbrey equation (change in resonance frequency α change in applied mass) is discussed. The Sauerbrey equation gives an accurate estimate of the film thickness, tf, only if (i) the film is thin compared to the shear-wave penetration depth, δ, into the liquid, i.e., tf ⪡ δ, and (ii) the film does not slide on the QCM electrode (s). We have shown that by measuring both the QCM resonance frequency and the dissipation factor simultaneously, the thickness range over which tf can be measured accurately can be extended to about 2δ for non-slipping films. If the film slips, which we have only observed for molecularly thin films, changes in dissipation factor can be used to calculate the coefficient of friction between the film and the substrate. We also show the usefulness of measuring the dissipation factor of the QCM when studying solid to liquid phase transitions.

325 citations


Journal ArticleDOI
TL;DR: A systematic framework of indicators for sustainability is presented in this article, where the authors focus on societal activities that affect nature and on the internal societal resource use, as opposed to environmental quality indicators.

Journal ArticleDOI
TL;DR: The results show that the contacting conductive liquid, in effect, enlarges the electrode area on the liquid side and thereby changes the parallel resonant frequency, and by proper design of the QCM measurement, perturbing effects due to the liquid's electrical properties can be circumvented.
Abstract: Recently, several reports have shown that when one side of a quartz crystal microbalance (QCM) is exposed to a liquid, the parallel (but not the series) resonant frequency is influenced by the conductivity and dielectric constant of the liquid. The effect is still controversial and constitutes a serious complication in many applications of the QCM in liquid environments. One suggestion has been that acoustically induced surface charges couple to charged species in the conducting liquid. To explore this effect, we have measured the parallel and the series mode resonance frequencies, and the corresponding Q factors, for a QCM with one side facing a liquid. These four quantities have all been measured versus liquid conductivity, using a recently developed experimental setup. It allows the simultaneous measurement of the resonant frequency and the Q factor of an oscillating quartz crystal, intermittently disconnected from the driving circuit. Based on these results, a simple model together with an equivalent circuit for a quartz crystal exposed to a liquid is presented. The analysis shows that it is not necessary to infer the existence of surface charges (or other microscopic phenomena such as electrical double layers) to account for the influence of the liquid's electrical properties on the resonant frequency. Our results show that the contacting conductive liquid, in effect, enlarges the electrode area on the liquid side and thereby changes the parallel resonant frequency. By proper design of the QCM measurement, perturbing effects due to the liquid's electrical properties can be circumvented.

Journal ArticleDOI
TL;DR: The destabilizing effects of a series of Na salts with various monovalent anions on N/3' PNA-DNA and Pna-PNA duplexes were found to follow the Hofmeister series, emphasizing the importance of the hydrophobic interaction between nucleobases for the stability of the PNA complexes in high salt concentration.
Abstract: Peptide nucleic acid (PNA) is a DNA analogue in which the negatively charged sugar phosphate backbone has been substituted by uncharged N-(2-aminoethyl)glycine units. The study of a PNA-DNA duplex and the corresponding DNA-DNA duplex gives a unique opportunity to compare two polyelectrolytes with virtually identical geometry but greatly different linear charge density. The results provide a basis for a study of the applicability of the Poisson-Boltzmann (PB) and counterion condensation (CC) theories. UV and circular dichroism spectroscopy as well as isothermal titration calorimetry (ITC) have been used to study the effect of different ions on the stability and conformation of PNA-DNA, PNA-PNA, and DNA-DNA duplexes having the same base sequences. Cations in general destabilize both antiparallel (N/3') and parallel (N/5') PNA-DNA duplexes whereas they stabilize the DNA-DNA duplex. Studies on the effect of monovalent salt such as NaCl on T-m were carried out over a wide range of salt concentrations (0.01 to 5 M). The decrease in the T-m of the N/3' PNA-DNA duplex with increasing ionic strength in the range of concentrations of 0.01 to 0.5 M, where electrostatic effects predominate, is explained in terms of counterion release upon duplex formation in contrast to the counterion association accompanying the formation of a DNA duplex. The uncharged PNA-PNA duplex shows no significant destabilization in this concentration range. The higher stability of the N/3' PNA-DNA compared to the DNA-DNA duplex (Delta Delta G similar to-7 kcal/mol) is ascribed to more favorable entropic contributions consistent with the counterion release that accompanies the PNA-DNA duplex formation. At high salt concentration (>1 M), where electrostatic contributions saturate, similar trends in the decrease in T-m, were observed for the three types of duplexes irrespective of their backbone charges. The destabilizing effects of a series of Na salts with various monovalent anions on N/3' PNA-DNA and PNA-PNA duplexes were found to follow the Hofmeister series, emphasizing the importance of the hydrophobic interaction between nucleobases for the stability of the PNA complexes in high salt concentration.

Journal ArticleDOI
TL;DR: The ability to simulate temperature, dispersion, and soft-breakdown effects as well as a new /spl alpha/ dependence was added to the Chalmers nonlinear model for high electron mobility transistor (HEMT) and metal semiconductor field effect transistor (MESFET's) in this paper.
Abstract: The ability to simulate temperature, dispersion, and soft-breakdown effects as well as a new /spl alpha/ dependence was added to the Chalmers nonlinear model for high electron mobility transistor (HEMT's) and metal semiconductor field-effect transistor (MESFET's). DC, pulsed dc, low frequency (10 Hz-10 MHz), RF, and small signal S-parameter measurements (1-18 GHz) have been made on a large number of commercial HEMT and MESFET devices from different manufacturers in the temperature range 17-400 K in order to evaluate the validity of the model extensions.

Journal ArticleDOI
TL;DR: Angle-resolved photoelectron spectroscopy has been used to directly prove the existence of a charge accumulation layer at clean InAs surfaces.
Abstract: Angle-resolved photoelectron spectroscopy has been used to directly prove the existence of a charge accumulation layer at clean InAs surfaces. The formation of an accumulation layer is shown to be a common property of polar InAs surfaces, with the precise surface Fermi level position above the conduction band minimum determined by the surface geometry. The emission from states in the accumulation layer is studied with respect to its photon energy and angular dependence.

Journal ArticleDOI
TL;DR: In this article, the authors carried out flow experiments and aperture measurements on the same specimen of a single natural fracture, in order to compare measured flow with predicted flow based on geometrical description of the fracture void space.

Journal ArticleDOI
TL;DR: In this article, the properties of surface oxides on titanium surfaces were discussed by discussing some selected examples of surface spectroscopy analyses of Ti surfaces prepared by different methods, including clinical procedures (machining, solvent cleaning, sterilization), electrochemical methods (electropolishing and anodic oxidation), thermal oxidation in air, and nitrogen-ion implantation.

Journal ArticleDOI
TL;DR: After 12 weeks insertion time in the rabbit tibia and femur, a higher removal torque and more bone-to-metal contact was found for the implants blasted with 75-microns particles compared with the 25-micron-blasted ones.
Abstract: A comparison was made between screw-shaped c.p. titanium implants blasted with either 25- or 75-microns particles of Al2O3. The implant surfaces were investigated with respect to topography and composition before implantation in rabbit bone. Grit blasting with 25- or 75-microns particles produced two different surface roughnesses, but no significant difference in the surface composition for the two surfaces. After 12 weeks insertion time in the rabbit tibia and femur, a higher removal torque and more bone-to-metal contact was found for the implants blasted with 75-microns particles compared with the 25-microns-blasted ones.

Journal ArticleDOI
TL;DR: In this paper, the authors reviewed the economics of global warming with special emphasis on how the cost depends on the discount rate and on how costs in poor and rich regions are aggregated into a global cost estimate.

Proceedings ArticleDOI
11 Dec 1996
TL;DR: In this article, the authors considered the stability and robustness issues for hybrid systems and proposed stronger conditions for stability, and formulated the search for Lyapunov functions as a linear matrix inequality problem.
Abstract: Stability and robustness issues for hybrid systems are considered in this paper. Present stability results, that are extensions of classical Lyapunov theory, are not straightforward to apply in general due to two reasons. First, existing theory do not unveil how to find needed Lyapunov functions. Secondly, at some time instants it is necessary to know the values of the continuous trajectory. Because of these drawbacks, stronger conditions for stability are suggested. The search for Lyapunov functions can then be formulated as a linear matrix inequality problem. Additionally, it is shown how to obtain robustness properties. An example illustrates the results.

Journal ArticleDOI
TL;DR: In this article, the absorption envelope of the metal-to-ligand charge transfer (MLCT) region has been resolved in a complex of this type bound to DNA by combined use of LD and emission anisotropy excitation spectra measured in highly viscous solution.
Abstract: Linear dichroism (LD) has been used to probe the binding geometries of the diastereomeric adducts between DNA and the Delta and Lambda enantiomers of [Ru(phen)(2)L](2+) where the chelate ligand L is either dipyrido[3,2-a:2',3'-c]-phenazine (DPPZ) or its benzologue benzodipyrido[a:3,2-h:2'3'-j]phenazine (BDPPZ). By combined use of LD and emission anisotropy excitation spectra measured in highly viscous solution the absorption envelope of the metal-to-ligand charge transfer (MLCT) region has been fur the first time resolved in a complex of this type bound to DNA. The absorption can be described by four effective polarization directions (three almost orthogonal), along one of which any transition is polarized, assignments which are in good agreement with molecular orbital (INDO/S) calculations. The analysis of the LD spectrum provides the orientation of the complex in terms of several angles. Near perpendicularity relative to the DNA helix axis, found for the in-plane long and short axes of BDPPZ and DPPZ, together with extensive hypochromicity of the corresponding intraligand transitions, supports intercalation of the (B)DPPZ ligands between the DNA bases as earlier studies have indicated. MLCT transition moments that make an oblique angle to the molecular plane of the (B)DPPZ chromophores confirm this orientation and, in addition, provide strong evidence for a rotation (roll) of the complex around the pseudo-dyad axis, The roll is small (varying between 5 and 15 degrees), but significant, and has the same sign (clockwise) for both enantiomeric forms of the two complexes studied and shows only minor variations between calf-thymus DNA and alternating GC or AT homopolymer duplexes, It may reflect a property intrinsic of DNA (tilt of bases) or be a result of steric interference of the two phenanthroline ''propeller blades'' with a groove. The roll provides the first example of an angle in a DNA system that has been determined with its sign from LD spectroscopy.

Journal ArticleDOI
TL;DR: The proposed discretization uses convolution quadrature based on the first- and second-order backward difference methods in time, and piecewise linear finite elements in space to study the numerical approximation of an integro-differential equation.
Abstract: We study the numerical approximation of an integro-differential equation which is intermediate between the heat and wave equations. The proposed discretization uses convolution quadrature based on the first- and second-order backward difference methods in time, and piecewise linear finite elements in space. Optimal-order error bounds in terms of the initial data and the inhomogeneity are shown for positive times, without assumptions of spatial regularity of the data.

Journal ArticleDOI
01 Dec 1996
TL;DR: The framework addresses the components which must be considered in providing effective visualisations and is specified using a declarative object oriented language; the resulting object model may be mapped to a variety of graphical user interface development platforms.
Abstract: In this paper we examine the issues involved in developing information visualisation systems and present a framework for their construction. The framework addresses the components which must be considered in providing effective visualisations. The framework is specified using a declarative object oriented language; the resulting object model may be mapped to a variety of graphical user interface development platforms. This provides general support to developers of visualisation systems. A prototype system exists which allows the investigation of alternative visualisations for a range of data sources.

Journal ArticleDOI
TL;DR: In this article, extensive research has been carried out regarding experiences of implementing of ISO 9000 in Swedish industry, where more than 50 per cent of the Swedish ISO 9000 companies certified in 1993 were investigated.
Abstract: In recent years, work to implement the ISO 9000 standard has been intensified in Swedish industry. A rapidly growing number of companies in various industries and lines of business have already been certified or are working towards certification. This situation is very interesting from the point of view of research, as it provides the opportunity to make observations in companies where the work towards change has been going on for a couple of years, at the same time as this work can be studied within new lines of business from the start. Recently, extensive research has been carried out regarding experiences of implementing of ISO 9000 in Swedish industry. Reports the results of this research. In an explorative phase, generates different research questions. Descriptive studies were then made based on these results. In addition, longitudinal in‐depth studies focusing on the management of change and based on case studies were carried out in this phase. In all, more than 50 per cent of the Swedish ISO 9000 companies certified in 1993 were investigated. Shows the most common reasons for certification, the positive and negative effects and the companies’ experiences of certification. On the basis of these results, and on earlier known models of change work, draws normative conclusions with implications for more efficient management of change.

Journal ArticleDOI
TL;DR: In this article, two austenitic stainless steels were polarized in 0.1 M HCl + 0.4 M NaCl at 22 and 65 °C, respectively, and the composition and thickness of the passive films formed during polarization to the potentials −75, + 500 and + 800 mV (SCE) were determined.

Journal ArticleDOI
TL;DR: An algorithm is described to obtain the slope correction from a SAR interferogram, which also enables retrieval of the full scattering geometry, and demonstrates that the spatial resolution and calibration error are adequate for most applications.
Abstract: The brightness in a SAR image is affected by topographic height variations due to (1) the projection between ground and image coordinates, and (2) variations in backscattering coefficient with the local scattering geometry. This paper derives a new equation for (1), i.e. the radiometric slope correction, based on a calibration equation which is invariant under a coordinate transformation. An algorithm is described to obtain the slope correction from a SAR interferogram, which also enables retrieval of the full scattering geometry. Since the SAR image and interferogram are derived from the same data set, there is no need to match the image with the calibration data. There is also no need for phase unwrapping since the algorithm only uses the fringe frequencies. A maximum-likelihood estimator for the fringe frequency is analyzed and the algorithm is illustrated by processing ERS-1 SAR data. The example demonstrates that the spatial resolution and calibration error are adequate for most applications.

Journal ArticleDOI
TL;DR: In this paper, it is found that the concrete compressive strength significantly affects the strength of the stud connections and that the present design code is not adequate to estimate the shear strength of studs embedded in high strength concrete and it is suggested that a design formula that takes account of the interaction between the studs and the surrounding concrete should be used.

Journal ArticleDOI
TL;DR: In this article, the authors derived a relation between the blockage width and the bistatic scattering width, and showed how cylinders such as struts and masts can be constructed to reduce their blockages.
Abstract: We discuss how forward scattering can he characterized in terms of an equivalent blockage width, and a relation between this and the bistatic scattering width is derived. Then, we show how cylinders such as struts and masts can be constructed to reduce their blockage widths. Thereby, when the cylinders are mounted in front of an antenna, the sidelobes and losses caused by the blockage will be reduced. For thin metal cylinders the blockage width reduction is obtained by giving its cross section an oblong shape and, in addition (for the TM case), by coating the outer metal surface with dielectric material to obtain a hard boundary condition. For thick cylinders, the reduced scattering is obtained by designing them as dielectric-filled parallel plate waveguides with the outer surfaces of the plates coated in the same way as for the thin struts. Dual-polarized performance is obtained in both cases by strip loading the outer surfaces. The performance of both the thin and the thick struts have limited frequency bandwidth. Both computed and measured results are presented; the computations being done with the moment method. The designs are based on the concept of soft and hard surfaces in electromagnetics, and the results can be regarded as a proof of the existence of hard surfaces for electromagnetic waves. The study considers reduction of forward scattering which also will give a reduction of the total integrated power of the scattered field over all directions-even backward.

Journal ArticleDOI
TL;DR: In this paper, the average efficiency of three 500 kW wind energy converters is compared, and it is shown that a variable-speed generator system can be almost as efficient as one for constant speed, although it has much higher losses at rated load.
Abstract: This paper presents a method to calculate the average efficiency from the turbine shaft to the grid in wind energy converters. The average efficiency of three 500 kW systems are compared. The systems are: a conventional grid-connected four-pole induction generator equipped with a gear, a variable-speed synchronous generator equipped with a gear and a frequency converter, and a directly driven variable-speed generator equipped with a frequency converter. In this paper it is shown that a variable-speed generator system can be almost as efficient as one for constant speed, although it has much higher losses at rated load. The increased turbine efficiency that variable speed leads to has not been included in this paper. It is also found that a directly driven generator can be more efficient than a conventional four-pole generator equipped with a gear.

Journal ArticleDOI
TL;DR: The spin-spin correlation function of the antiferromagnetic spin-\textonehalf{} chain is calculated numerically in the presence of a next-nearest-neighbor coupling for chains of up to 32 sites to unambiguously confirm the field theory predictions.
Abstract: Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model, the spin-\textonehalf{} chain, these corrections have been controversial. In this paper, the spin-spin correlation function of the antiferromagnetic spin-\textonehalf{} chain is calculated numerically in the presence of a next-nearest-neighbor coupling ${J}_{2}$ for chains of up to 32 sites. By varying the coupling strength ${J}_{2}$ we can control the effect of the marginal operator, and our results unambiguously confirm the field theory predictions. The critical value at which the marginal operator vanishes has been determined to be at $\frac{{J}_{2}}{J}=0.241167\ifmmode\pm\else\textpm\fi{}0.000005$.