Browsing M.Sc. Physics by Title
Now showing items 1938 of 110

Dechanneling of 2 Mev Heâ ½ in goldThick gold single crystals of high quality were prepared for Rutherford Backscattering Dechanneling studies by electropolishing and annealing. The variation.; with temperature of the Random Fraction versus Depth spectrtnn for 2 MeV He+ on < 110> gold was extracted from measured Aligned and Random (Energy) Spectra. The measured dechanneling rate showed a sixfold increase in going from 4loK to 293°K and is in reasonable agreement with calculations made using the Steady Increase in Transverse Energy (SITE) approximation.

Deformations of Maxwell gauge field theoryDeformations of Maxwell gauge theory are studied in 2+1 dimensions. Unlike in previous work in the literature, no Lagrangian structure is assumed for possible deformations, and instead the requirement of gauge invariance of the deformed field equations under the deformed gauge symmetry is used. The results yield a new nonlinear generalization of Maxwell gauge theory. A nonabelian extension of this theory is also obtained.

The design of a reflectance spectrometer and its calibration using SrTiO3 /A new UltraHigh Vacuum (UHV) reflectance spectrometer was successfully designed, making use of a Janis Industries ST400 sample cryostat, IR Labs bolometer, and Briiker IFS 66 v/S spectrometer. Two of the noteworthy features include an in situ gold evaporator and internal reference path, both of which allow for the experiment to progress with a completely undisturbed sample position. As tested, the system was designed to operate between 4.2 K and 325 K over a frequency range of 60  670 cm~^. This frequency range can easily be extended through the addition of appUcable detectors. Tests were performed on SrTiOa, a highly ionic incipient ferroelectric insulator with a well known reflectance. The presence and temperatmre dependence of the lowest frequency "soft" mode were measured, as was the presence of the other two infrared modes. During the structural phase transition from cubic to tetragonal perovskite, the splitting of the second phonon mode was also observed. All of the collected data indicate good agreement with previous measurements, with a minor discrepency between the actual and recorded sample temperatures.

Design of Resistivity Instrumentation for a He3 Cryostat and its Application to the Charge Density Wave Superconductor CuxTiSe2Fermi patches in quasitwo dimensional charge density waves (CDW) have not described the connection to superconductivity (SC) according to theory adequately at this point in time. The connection between CDW and SC in the quasitwo dimensional material CuxTiSe2 is an interesting one which might reveal mechanisms in unconventional superconductors. A previous Brock graduate student grew crystals of CuxTiSe2. The precise doping of the samples was not known. In order to determine the doping parameter x in CuxTiSe2, a sensitive resistivity measurement system was necessary. A new resistivity measurement system was designed and implemented utilizing an Infrared Labs HDL10 He3 cryostat. By comparing with data from the literature, doping of two samples was investigated using the new measurement system and a Quantum Design Magnetic Property Measurement System (MPMS). Methods for determining the doping revealed that the old resistivity system would not be able to determine the CDW transition temperature of highly doped samples or doping for elongated samples due to electronic noise. Doping in one sample was found to be between x=0.06 and x=0.065. Values of doping in the second sample had a discrepancy but could be explained by incorrect sample orientation.

Developing a numerical inversetheorybased extraction of orientationdependent relaxation rates from partially relaxed spectraSecondrank tensor interactions, such as quadrupolar interactions between the spin 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically illposed problem. However, numerical methods (dePakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a threeterm truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a secondrank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, modelfree

Diffusion Monte Carlo study of electronic properties for H and Be atoms /We examined three different algorithms used in diffusion Monte Carlo (DMC) to study their precisions and accuracies in predicting properties of isolated atoms, which are H atom ground state, Be atom ground state and H atom first excited state. All three algorithms — basic DMC, minimal stochastic reconfiguration DMC, and pure DMC, each with futurewalking, are successfully impletmented in ground state energy and simple moments calculations with satisfactory results. Pure diffusion Monte Carlo with futurewalking algorithm is proven to be the simplest approach with the least variance. Polarizabilities for Be atom ground state and H atom first excited state are not satisfactorily estimated in the infinitesimal differentiation approach. Likewise, an approach using the finite field approximation with an unperturbed wavefunction for the latter system also fails. However, accurate estimations for the apolarizabilities are obtained by using wavefunctions that come from the timeindependent perturbation theory. This suggests the flaw in our approach to polarizability estimation for these difficult cases rests with our having assumed the trial function is unaffected by infinitesimal perturbations in the Hamiltonian.

The diffusion of Coâ ¶æº© Zrâ â Tiâ â alloy /nS. Kumar.  260 St Catharines [Ont.] : Dept. of Physics, Brock University,The diffusion of Co60 in the body centered cubic beta phase of a ZrSOTi SO alloy has been studied at 900°, 1200°, and 1440°C. The results confirm earlier unpublished data obtained by Kidson17 • The temperature dependence of the diffusion coefficient is unusual and suggests that at least two and possibly three mechanisms may be operative Annealing of the specimen in the high B.C.C. region prior to the deposition of the tracer results in a large reduction in the diffusion coefficient. The possible significance of this effect is discussed in terms of rapid transport along dislocation network.

Effect of rattling Phonons on Superconductivity of KOs_2O_6We model the electron coupling to anharmonic (rattling) mode in βpyrochlore superconductor KOs2O6 by a sharply peaked electronphonon coupling function α2F(Ω) centered at the mode energy. The strongcoupling Eliashberg equations are solved for the transition temperature Tc and the gap function ∆(ω,T) for a series of temperatures 0 < T < Tc. From these solutions, we obtain the temperature dependence of the gap edge ∆(T), the nuclear magnetic resonance (NMR) relaxation rate and the microwave conductivity for several values of the electronphonon coupling parameter λ. The results are compared with the available experimental results 0 for KOs2O6

Effect of the position of the doublebond in monounsaturated phospholipids on the dynamics of model membranesTherllloelynalllics of lllodel 11lel1ll)rane systeills containing 1110nollnsaturatecl I)lloSI)holil) ids is strongly infllienced l)y the I)osition of the C==C dOlll)le })ond in tIle acyl chain. The telllI)eratllres of both chainnlelting (TM) and La + HI! (TH) I)hase traIlsitions are lowered by IIp to 20°C when C==C is Inoved froln positions 6 or 11 to I)osition 9 in an 18carl)on chain. This work is an attellll)t to ellicidate the uIlderlying Illoleclilar Illechanisllls reSI)Onsi])le for tllese draillatic tllerillodynaillic changes. Mixtllres of di18: 1 l)hoSI)hatidylethanolanline with C==C at l)ositioIlS 6, 9, 11 were llsed, witll a sI1lall aI1lOlint of I)erdellterated tetradecanol, known to })e a gooel rel)Orter of the cllain Illoleclilar order. SI)ectral second 11I0I1lents were llsed to Illonitor tIle La + HII I)hase transition, which was fOllnd to ])e ])road (26°C), with a slight llysteresis on heatiIlg/cooling. The orientational order I)rofiles were nleasllred 1lSiIlg 2H Illiclear Illagnetic resonance and changes in these order I)rofiles between La aIld HII I)hases silow l)oth a local increase in order in the vicinity of the C==C bonds and an o\Terall decrease ill the average orientational order of the chain as a whole. These Sll])tle changes recluire })oth highfidelity SI)ectrosCol)y and a careflll data analysis that takes into aCCOllnt the effects due to l)artiall1lagneticallyindllced orientational ordering of the l)ilayers. In tIle COIltext of SOllle recently rel)Orted crossrelaxation 11leaSlirenlents in Silllilar l)llOSI)llolil)iels, 0111' reslilts sllggest that largeanll)litllde conforlllational changes in the interior of tIle I110del 111eI11])ranes I)lay a 1110re significant role than I)reviollsly thOllght.

Effect of Topological Morphology on Optical Filtering Properties of Porous SiliconMacroporous silicon samples of differing topological porous properties were manufactured by way of electrochemical etching. Different etching parameters (etching current, time, electrolyte concentration) were used on four different (in terms of crystal orientation and resistivity) types of samples in order to obtain a series of samples of differing pore topology. It is known that macroporous silicon acts as a highwavelength pass filter in the infrared regime. FTIR spectroscopy was performed on each of these samples in order to obtain an optical cutoff wavenumber for each sample. Furthermore, SEM analysis was performed in order to determine the number of pores per unit area on the surface as well as the percentage of the surface that was covered in pores for each sample. Furthermore, the average linear dimension per pore was determined using these values. Finally, the average poretopore distance was also estimated on each sample. These four sets of measurements were performed in order to find a relationship between the optical and topological properties of macroporous silicon. It was found that there is a relationship between pore number density and cutoff; the cutoff wavenumber increases as the pore number density is increased. Additionally, a correlation between the pore spacing and the cutoff was also determined; the cutoff wavelength increases as the pore spacing increases. It was expected that there would be a correlation between the average linear dimension per scattering element as is seen in other types of scattering filters; however such a trend was only observed for one of the sample types. This suggests that the scattering mechanism by which porous silicon filters operate differs between samples of significantly differing surface topology. In addition to this, the temperaturedependence of the cutoff was investigated. Through lowtemperature optical analysis using FTIR spectroscopy and liquid helium as a coolant, it was determined that the cutoff wavenumber exhibits no temperaturedependence below 100 K. For higher temperatures, the measurements performed were inconclusive. This was due to the thermal expansion at higher temperatures of the copper sample holder coupled with the inhomogeneity of the surface structure of each of the silicon filters.

The Effects of Annealing URu2Si2 on the Resistivity and Meissner EffectThe enigmatic heavy fermion URu2Si2, which is the subject of this thesis, has attracted intensive theoretical and experimental research since 1984 when it was firstly reported by Schlabitz et al. at a conference [1]. The previous bulk property measurements clearly showed that one second order phase transition occurs at the Hidden Order temperature THO ≈ 17.5 K and another second order phase transition, the superconducting transition, occurs at Tc ≈ 1 K. Though twenty eight years have passed, the mechanisms behind these two phase transitions are still not clear to researchers. Perfect crystals do not exist. Different kinds of crystal defects can have considerable effects on the crystalline properties. Some of these defects can be eliminated, and hence the crystalline quality improved, by annealing. Previous publications showed that some bulk properties of URu2Si2 exhibited significant differences between asgrown samples and annealed samples. The present study shows that the annealing of URu2Si2 has some considerable effects on the resistivity and the DC magnetization. The effects of annealing on the resistivity are characterized by examining how the Residual Resistivity Ratio (RRR), the fitting parameters to an expression for the temperature dependence of the resistivity, the temperatures of the local maximum and local minimum of the resistivity at the Hidden Order phase transition and the Hidden Order Transition Width ∆THO change after annealing. The plots of one key fitting parameter, the onset temperature of the Hidden Order transition and ∆THO vs RRR are compared with those of Matsuda et al. [2]. Different media used to mount samples have some impact on how effectively the samples are cooled because the media have different thermal conductivity. The DC magnetization around the superconducting transition is presented for one unannealed sample under fields of 25 Oe and 50 Oe and one annealed sample under fields of 0 Oe and 25 Oe. The DC field dependent magnetization of the annealed Sample11 shows a typical field dependence of a TypeII superconductor. The lower critical field Hc1 is relatively high, which may be due to flux pinning by the crystal defects.

Electrogenic proton/Lglutamate symport in isolated asparagus sprengeri mesophyll cellMedium' alkaliniiation occurred lipon the addition of LGlu to mechanically isolated Asparagus sprengeri mesophyll cells suspended in 1 mM CaS04. Alkalinization resulted from the coupled entry of H+ and LGlu anion into the cells. This H+ ILGlu symport did not stimulate K+ efflux. K+ efflux has been observed during H~ lamino acid symport in other systems. The stimulation of K+ efflux by proton coupled symport is regarded as an indicator of a plasma membrane depolarizing electrogenic symport process. H+ ILGlu symport in Asparagus sprengerimesophyl1 cells was investigated to determine whether or not the process was electrogenic. The rate of uptake of 0.25 11M 3HMTPP+ ( Methyltriphenylphosphonium, methyl3H ) is a probe for monitoring changes in the membrane potential. 3HMTPP+ uptake was reduced by K+ or CCCP, agents known to depolarize the membrane potential. Uptake of 3HMTPP+ was also inhibited by LGlu but not by DGlu. Conversely, 10 mM external MTPP+ inhibited the uptake of 14CULGlu. Simultaneous measurements of the rates of 14CULGlu uptake and LGlu dependent H+ influx showed that the molar stoichiometry of H+ ILGlu symport was 2 to 1. K+ or Na+ stimulated H+ efflux was completely inhibited by DCCD, DES, oligomycin and antimycin reagents which inhibit ATP driven H+ efflux. The H+ efflux \Vas also stimulate.d by the weak acids, butyric acid and acetic acid, which are known foaCidify the cytoplasm. This weak acid stimulated H+ efflux was also completely inhibited by oligomycin. It was calculated that net LGlu dependent H+ influx increased by 100% in the presence of oligomycin and that despite net medium alkalinization H+ ILGlu symport stimulates ATP dependent H+ efflux. 11 The data presented in this study indicate that H+ ILGlu symport is electrogenic. The data also show that ATP dependent Ht efflux rather than K+ efflux is the process compensating for thi~ electrogenic H+ ILGlu symport.

Electronic and magnetic properties of LaV1xO3 /A series of LaVi^xOs compounds (x=0.00, 0.02, 0.04, 0.06, 0.08) were prepeired using the standard solid reaction. The samples were chareicterized by Xray diffraction (XRD), fourprobe resistivity, smd magnetic susceptibility studies. Powder Xray diffraction analysis indicated the formation of a singlephase sample with a orthorhombic structure which was first found in GdFeOs (space group Pnma) . The Unit Cell program was used for calculating lattice peirameters from XFID data. The XRD spectnim could be indexed on a cubic lattice with Og = 2ap ~ (7.8578 to 7.9414 A). The lattice parameter was observed to increase as the Vanadium vacancy increased. Fourprobe resistivity measurements exhibited semiconductor behavior for all sajnples from room temperature down to 19K. The resistivity of samples increased with increasing Vanadium vacancy. The resistivity of samples demonstrated activated conduction with an activation energy of approximately 0.2 eV. The activation energy increased with increasing lattice parameter. Field cool magnetic susceptibility measurements were performed with field of 500 G from 300 K to 5 K. These measurements indicated the presence of an antiferromagnetic transition at about 140 K. The data was fitted above Neel temperature to CiurieWeiss law yielding a negative parameignetic Curie temperature. This implies that antiferromagnetic ordering is present.

Electronic and Magnetic Properties of MAX Phase (Cr1xGdx)2AlC and Er3AlC AlloyBulk samples of (Cr1xGdx)2AlC with X = 0, 0.0025, 0.01, 0.025, 0.05 and Er3AlC compound were synthesized using the arc melting technique. The samples were characterized by Xray diffraction, magnetic susceptibility, and four probe resistivity measurements to study their magnetic and electronic properties. Using Rietveld analysis for Xray diffraction, it was determined that the parent compound Cr2AlC exhibits a side phase of Cr7C3. The substituted samples were found to have secondary phases of Cr7C3 and GdCr3.5Al8.5 which slightly increase on increasing substitution of Cr3+ by Gd3+. The change of the concentration of Gadolinium does not have any real effect on the lattice parameter of (Cr1xGdx)2AlC. Er3AlC contains secondary phases of ErAl2 and ErC0.6. The MAX phase Cr2AlC and the Gadolinium substituted samples show complex magnetic behaviour. The magnetization measurements show that Cr2AlC has an unusual magnetic behavior above 70 K which does not obey the CurieWeiss law. The sample with X = 0.0025 also does not obey the CurieWeiss law at high temperature. The susceptibility data shows that samples with X = 0.01, 0.025, and 0.05 obey the CurieWeiss law, and the magnitude of the effective magnetic moments decreases while increasing the value of X. The susceptibility data of Er3AlC obey the CurieWeiss law; and the effective moment is 9.1 ± 0.005 𝛍B. The resistivity measurement of the parent sample Cr2AlC indicates metallic behavior. In the Gdsubstituted samples, we observed a Kondo Effect from the resistivity data. The resistivity of Gdsubstituted samples increases with increasing Gadolinium concentration. We also observed metallic behavior in the Er3AlC resistivity.

Electronic and Magnetic Properties of Pyrochlore (Eu(1x)Dyx)2Ir2O7The pyrochlore (Eu(1x)Dyx)2Ir2O7 for x = 0, 0.25, 0.50, 0.75, and 1.0 were prepared using solidstate reaction method. As the Dy concentration increases, the Xray results indicate a systematic decrease of the cubic lattice parameter of (Eu(1x)Dyx)2Ir2O7. We observed metal insulator transition in all compounds in addition two new anomalies at high temperatures in specifi c heat and resistivity results. The origin of these anoma lies have not yet been identifi ed. The metal insulator transition temperature TMI of (Eu(1x)Dyx)2Ir2O7 increases with the reduction in the lattice parameter. In the mag netic susceptibility results, the effective magnetic moment increases with the increment of the Dy substitution for Eu ions. The magnetic fi eld dependence of resistivity was in vestigated for all samples, negative and positive magnetoresistance effects are discussed.

Electronic, magnetic and thermal properties of Pb₂₋x AxCrO₅ (A = K or La)Lead chromium oxide is a photoconductive dielectric material tha t has great potential of being used as a room temperature photodetector. In this research, we made ceramic pellets of this compound as well as potassium doped compound Pb2xKxCr05, where x=O, 0.05, 0.125. We also investigate the properties of the lanthanum doped sample whose chemical formula is Pb1.85Lao.15Cr05' The electronic, magnetic and thermal properties of these materials have been studied. Magnetization measurements of the Pb2Cr05 sample indicate a transition at about 310 K, while for the lanthanum doped sample the transition temperature is at about 295 K indicating a paramagnetic behavior. However, the potassium doped samples are showing the transition from paramagnetic state to diamagnetic state at different temperatures for different amounts of potassium atoms present in the sample. We have studied resistivity as a function of temperature in different gas environments from 300 K to 900 K. The resistivity measurement of the parent sample indicates a conducting to insulating transition at about 300 K and upon increasing the temperature further, above 450 K the sample becomes an ionic conductor. As temperature increases a decrease in resistance is observed in the lanthanum/potassium doped samples. Using Differential Scanning Calorimetry experiment an endothermic peak is observed for the Pb2Cr05 and lanthanum/potassium doped samples at about 285 K.

Elucidation of a mechanism of cell lysis by chorhexidine : a biophysical approachChlorhexidine is an effective antiseptic used widely in disinfecting products (hand soap), oral products (mouthwash), and is known to have potential applications in the textile industry. Chlorhexidine has been studied extensively through a biological and biochemical lens, showing evidence that it attacks the semipermeable membrane in bacterial cells. Although extremely lethal to bacterial cells, the present understanding of the exact mode of action of chlorhexidine is incomplete. A biophysical approach has been taken to investigate the potential location of chlorhexidine in the lipid bilayer. Deuterium nuclear magnetic resonance was used to characterize the molecular arrangement of mixed phospholipid/drug formulations. Powder spectra were analyzed using the dePakeing technique, a method capable of extracting both the orientation distribution and the anisotropy distribution functions simultaneously. The results from samples of protonated phospholipids mixed with deuteriumlabelled chlorhexidine are compared to those from samples of deuterated phospholipids and protonated chlorhexidine to determine its location in the lipid bilayer. A series of neutron scattering experiments were also conducted to study the biophysical interaction of chlorhexidine with a model phospholipid membrane of DMPC, a common saturated lipid found in bacterial cell membranes. The results found the hexamethylene linker to be located at the depth of the glycerol/phosphate region of the lipid bilayer. As drug concentration was increased in samples, a dramatic decrease in bilayer thickness was observed. Differential scanning calorimetry experiments have revealed a depression of the DMPC bilayer geltolamellar phase transition temperature with an increasing drug concentration. The enthalpy of the transition remained the same for all drug concentrations, indicating a strictly drug/headgroup interaction, thus supporting the proposed location of chlorhexidine. In combination, these results lead to the hypothesis that the drug is folded approximately in half on its hexamethylene linker, with the hydrophobic linker at the depth of the glycerol/phosphate region of the lipid bilayer and the hydrophilic chlorophenyl groups located at the lipid headgroup. This arrangement seems to suggest that the drug molecule acts as a wedge to disrupt the bilayer. In vivo, this should make the cell membrane leaky, which is in agreement with a wide range of bacteriological observations.

Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration /Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate the exact expectation values, ($o^^o), of multiplicative operators, such as polarizabilities and highorder hyperpolarizabilities, for isolated atoms and molecules. The existing forwardwalking pure diffusion Monte Carlo (FWPDMC) algorithm which attempts this has a serious bias. On the other hand, the DMC algorithm with minimal stochastic reconfiguration provides unbiased estimates of the energies, but the expectation values ($o^^) are contaminated by ^, an user specified, approximate wave function, when A does not commute with the Hamiltonian. We modified the latter algorithm to obtain the exact expectation values for these operators, while at the same time eliminating the bias. To compare the efficiency of FWPDMC and the modified DMC algorithms we calculated simple properties of the H atom, such as various functions of coordinates and polarizabilities. Using three nonexact wave functions, one of moderate quality and the others very crude, in each case the results are within statistical error of the exact values.

An experimental investigation of dechanneling in copper single crystalsThis investigation comprises a comparison of experimental and theoretical dechanneling of MeV protons in copper single crystals. Dechanneling results when an ion's transverse energy increases to the value where the ion can undergo small impact parameter collisions with individual atoms. Depth dependent dechanneling rates were determined as functions of lattice temperature, ion beam energy and crystal axis orientation. Ion beam energies were IMeV and 2MeV,temperatures ranged from 35 K to 280 K and the experiment was carried out along both the (lOa) and <110) axes. Experimental data took the form of aligned and random Rutherford backscattered energy spectra. Dechanneling rates were extracted from these spectra using a single scattering theory that took explicit account of the different stopping powers experienced by channeled and dechanneled ions and also included a correction factor to take into account multiple scattering effects along the ion's trajectory. The assumption of statistical equilibrium and small angle scattering of the channeled ions allows a description of dechanneling in terms of the solution of a diffusion like equation which contains a so called diffusion function. The diffusion function is shown to be related to the increase in average transverse energy. Theoretical treatments of increase in average transverse energy due to collisions of projectiles with channel electrons and thermal perturbations in the lattice potential are reviewed. Using the diffusion equation and the electron density in the channel centre as a fitting parameter dechanneling rates are extracted. Excellent agreement between theory and experiment has been demonstrated. Electron densities determined in the fitting procedure appear to be realistic. The surface parameters show themselves to be good indicators of the quality of the crystal.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C^^C correlation spectroscopy under the magicangle spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the socalled Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly modeldependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constanttime doublequantumfiltered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a wellknown method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently twodimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signaltonoise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.