A procedure yielding to the determination of the low-frequency dynamical behavior of glass-forming systems with low glass transition temperature is presented in this paper. The liquids are injected in an inorganic porous medium and the mechanical response of the heterogeneous composite samples is studied. It is shown that the dynamic behavior of the liquid is poorly affected by the presence of the substrate. This enables to build the long-time relaxation diagram for maltitol, sorbitol and LiCl, 6H 2 O. The mechanical measurements are interpreted in the framework of a model based on the assumptions of localized disorder (defects) and hierarchically constrained dynamics in the glass transition region.
{"title":"Study of the α-Mechanical Relaxation in Molecular Glass-Forming Liquids","authors":"A. Faivre, L. David, J. Pérez","doi":"10.1051/JP2:1997207","DOIUrl":"https://doi.org/10.1051/JP2:1997207","url":null,"abstract":"A procedure yielding to the determination of the low-frequency dynamical behavior of glass-forming systems with low glass transition temperature is presented in this paper. The liquids are injected in an inorganic porous medium and the mechanical response of the heterogeneous composite samples is studied. It is shown that the dynamic behavior of the liquid is poorly affected by the presence of the substrate. This enables to build the long-time relaxation diagram for maltitol, sorbitol and LiCl, 6H 2 O. The mechanical measurements are interpreted in the framework of a model based on the assumptions of localized disorder (defects) and hierarchically constrained dynamics in the glass transition region.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"8 1","pages":"1635-1650"},"PeriodicalIF":0.0,"publicationDate":"1997-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81946944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Z. Radlinska, T. Gulik‐Krzywicki, F. Lafuma, D. Langevin, W. Urbach, C. Williams
The microstructure of a ternary system of a non-ionic surfactant (n–dodecyl pentaoxyethylene glycol ether, C12E5), water and a water-soluble random heteropolymer, poly (styrene-r-Na styrene sulfonate) with degrees of sulfonation ranging from 30% to 90% is investigated at room temperature. Using small angle X-ray scattering and freeze-fracture electron microscopy we focus on the lamellar phase region and study samples along four different paths of constant surfactant-to-water ratio with increasing polymer content. We demonstrate that for samples with low water content (S/W ratios 3.4 and 4.9), regardless of the sulfonation degree of the polymer, the lamellar phase persists up to several weight percent of polymer and the polymer molecules are confined inside the surfactant bilayers. With increasing quantity of polymer the lamellar phase Bragg peak shifts in a manner consistent with the increase of the lamellar period, which indicates increased bilayer thickness. For mixtures less concentrated in surfactant first order phase transitions are observed for all polymer charge contents when the amount of polymer is increased. For low charge contents of polymer (30% and 45%) the lamellar stack of the polymer-doped surfactant bilayers coexists with either cubic or another lamellar phase and microscopic phase separation is only observed. For large charge contents (65% and 90%) a surfactant-rich lamellar phase coexists with a polymer-rich water solution. It is suggested that the observed phase behaviour is governed by the concentration number of free water molecules.
{"title":"Modification of the Lamellar Phase in C12E5/Water System by a Random Hydrophilic-Hydrophobic Polyelectrolyte","authors":"E. Z. Radlinska, T. Gulik‐Krzywicki, F. Lafuma, D. Langevin, W. Urbach, C. Williams","doi":"10.1051/JP2:1997193","DOIUrl":"https://doi.org/10.1051/JP2:1997193","url":null,"abstract":"The microstructure of a ternary system of a non-ionic surfactant (n–dodecyl pentaoxyethylene glycol ether, C12E5), water and a water-soluble random heteropolymer, poly (styrene-r-Na styrene sulfonate) with degrees of sulfonation ranging from 30% to 90% is investigated at room temperature. Using small angle X-ray scattering and freeze-fracture electron microscopy we focus on the lamellar phase region and study samples along four different paths of constant surfactant-to-water ratio with increasing polymer content. We demonstrate that for samples with low water content (S/W ratios 3.4 and 4.9), regardless of the sulfonation degree of the polymer, the lamellar phase persists up to several weight percent of polymer and the polymer molecules are confined inside the surfactant bilayers. With increasing quantity of polymer the lamellar phase Bragg peak shifts in a manner consistent with the increase of the lamellar period, which indicates increased bilayer thickness. For mixtures less concentrated in surfactant first order phase transitions are observed for all polymer charge contents when the amount of polymer is increased. For low charge contents of polymer (30% and 45%) the lamellar stack of the polymer-doped surfactant bilayers coexists with either cubic or another lamellar phase and microscopic phase separation is only observed. For large charge contents (65% and 90%) a surfactant-rich lamellar phase coexists with a polymer-rich water solution. It is suggested that the observed phase behaviour is governed by the concentration number of free water molecules.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"29 1","pages":"1393-1416"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76686255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Brockbank, J. M. Huntley, J. M. Huntley, R. Ball
A simple elasto-optical method has been used to measure the normal force distribution under three-dimensional conical piles, for a range of granular materials. The method is based on the measurement of contact diameters of a monolayer of steel balls between the pile and an elastomeric substrate. Experiments on sandpiles confirm the existence of counterintuitive dips in the pressure at the centre of the pile, as reported previously in the literature; the dips were also found in piles of small (ca. 180 pm diameter) glass beads. They were suppressed, however, on increasing the glass bead diameter by a factor of ca. 3. Variations in surface roughness were found to have little effect on the pressure profiles. The probability density function for the normal contact force was approximately negative exponential in form.
{"title":"Contact Force Distribution Beneath a Three-Dimensional Granular Pile","authors":"R. Brockbank, J. M. Huntley, J. M. Huntley, R. Ball","doi":"10.1051/JP2:1997200","DOIUrl":"https://doi.org/10.1051/JP2:1997200","url":null,"abstract":"A simple elasto-optical method has been used to measure \u0000the normal force distribution under three-dimensional conical piles, for a range of granular materials. The method \u0000is based on the measurement of contact diameters of \u0000a monolayer of steel balls between the pile and an \u0000elastomeric substrate. Experiments on sandpiles confirm the existence of counterintuitive dips in the pressure at the centre of the pile, as reported previously in the literature; the dips were also found in piles of small (ca. 180 pm diameter) glass beads. They were suppressed, however, \u0000on increasing the glass bead diameter by a factor of \u0000ca. 3. Variations in surface roughness were found to have little effect on the pressure profiles. The probability density function for the normal contact force was \u0000approximately negative exponential in form.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"29 1","pages":"1521-1532"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88896903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Lecommandoux, L. Noirez, M. Achard, F. Hardouin
Un polymorphisme de type nematique - smectique C a ete pour la premiere fois revele dans les polymeres cristaux liquides en haltere. Des resultats structuraux et conformationnels obtenus par diffusion coherente de neutrons sont presentes pour les deux mesophases. Une inversion de la conformation de la chaine polymere est observee de la phase nematique a la phase smectique C. Ce comportement original est compare au cas de la transition N - S A pour des polymeres cristaux liquides en peigne.
在哑铃液晶聚合物中首次发现了向列-近晶C型多态性。通过相干中子扩散得到的结构和构象结果存在于两个中相中。从向列相到近晶c相，聚合物链的构象发生了逆转。将这种原始行为与梳状液晶聚合物的N - S a转变情况进行了比较。
{"title":"What about the Backbone Conformation in Nematic and Smectic C Phases of a ``Side-on'' Fixed LCP? A SANS Study","authors":"S. Lecommandoux, L. Noirez, M. Achard, F. Hardouin","doi":"10.1051/JP2:1997194","DOIUrl":"https://doi.org/10.1051/JP2:1997194","url":null,"abstract":"Un polymorphisme de type nematique - smectique C a ete pour la premiere fois revele dans les polymeres cristaux liquides en haltere. Des resultats structuraux et conformationnels obtenus par diffusion coherente de neutrons sont presentes pour les deux mesophases. Une inversion de la conformation de la chaine polymere est observee de la phase nematique a la phase smectique C. Ce comportement original est compare au cas de la transition N - S A pour des polymeres cristaux liquides en peigne.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"98 1","pages":"1417-1424"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72908392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss the possibility of Kelvin-Helmholtz instability of a Langmuir monolayer. Even for a positive surface tension, this instability is expected to occur above a critical value of the velocity of the upper air relative to the water. This is in contrast to the buckling transition which occurs for a negative surface tension.
{"title":"Kelvin-Helmholtz instability of Langmuir monolayers","authors":"S. Komura, T. Iwayama","doi":"10.1051/JP2:1997189","DOIUrl":"https://doi.org/10.1051/JP2:1997189","url":null,"abstract":"We discuss the possibility of Kelvin-Helmholtz instability of a Langmuir monolayer. Even for a positive surface tension, this instability is expected to occur above a critical value of the velocity of the upper air relative to the water. This is in contrast to the buckling transition which occurs for a negative surface tension.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"17 1","pages":"1331-1335"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78681123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dans un cristal liquide cholesterique pris en sandwich entre deux lames de verres conductrices avec des conditions d'ancrage homeotrope, l'apparition de structures spatiales isolees, appelees doigts cholesteriques de premiere espece, est maintenant bien comprise. Quand on soumet le cristal liquide a un champ electrique vertical, on observe alors que ces doigts cholesteriques se mettent a bouger perpendiculairement a son grand axe avec une vitesse V⊥. Dans ce papier, on montre analytiquement que cette vitesse pourrait etre reliee a l'effet Lehmann, et que sa mesure permettrait alors d'estimer la valeur du coefficient de couplage electromecanique.
{"title":"Is the electromechanical coupling the driving force for the perpendicular drift of first class cholesteric finger","authors":"L. Gil, S. Thiberge","doi":"10.1051/JP2:1997198","DOIUrl":"https://doi.org/10.1051/JP2:1997198","url":null,"abstract":"Dans un cristal liquide cholesterique pris en sandwich entre deux lames de verres conductrices avec des conditions d'ancrage homeotrope, l'apparition de structures spatiales isolees, appelees doigts cholesteriques de premiere espece, est maintenant bien comprise. Quand on soumet le cristal liquide a un champ electrique vertical, on observe alors que ces doigts cholesteriques se mettent a bouger perpendiculairement a son grand axe avec une vitesse V⊥. Dans ce papier, on montre analytiquement que cette vitesse pourrait etre reliee a l'effet Lehmann, et que sa mesure permettrait alors d'estimer la valeur du coefficient de couplage electromecanique.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"141 3 1","pages":"1499-1508"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77229273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent Neutron Scattering experiments by Richter et al. [1] show that the presence of coil-crystalline block copolymer (PE-PEP) micelles in a mixed alkane bath suppresses the crystallization out of solution of the long alkane component at low temperatures. Motivated by these experiments, we study theoretically the thermodynamics and kinetics of lamellar coil-crystalline block copolymer micelles in a bimodal solvent to better understand the factors determining the anti-precipitation action of coil-crystalline block copolymers. We assume an Alexander-de Gennes brush model for the strongly stretched corona chains and explicitly account for the polydispersity of the solvent chains. For the thermodynamic distribution of solvent chains in the corona, we find a predominance of short solvent chains to long solvent chains in the corona phase compared to the solvent bath, both with and without nematic interactions in the corona phase. We also calculate the rate of crystallization of the long solvent chains onto the micellar crystal core and find that the rate is sensitive to both brush and core parameters. In particular, we predict that to maximize the rate, both E fold /kTN A and X n need to be made as small as possible, where E fold is the folding energy of the crystal core chains, N A the number of statistical segments of the solvated corona chains and X n parameterises the strength of nematic interactions in the micellar corona. This leads to the surprising result that for fixed E fold , the rate of crystallization is increased when we increase the molecular weight of the corona blocks.
{"title":"Modification of the Crystallization Kinetics of a Mixed Bath of Alkanes in the Presence of Coil-Crystalline Block Copolymer Micelles","authors":"D. Buzza, T. McLeish","doi":"10.1051/JP2:1997192","DOIUrl":"https://doi.org/10.1051/JP2:1997192","url":null,"abstract":"Recent Neutron Scattering experiments by Richter et al. [1] show that the presence of coil-crystalline block copolymer (PE-PEP) micelles in a mixed alkane bath suppresses the crystallization out of solution of the long alkane component at low temperatures. Motivated by these experiments, we study theoretically the thermodynamics and kinetics of lamellar coil-crystalline block copolymer micelles in a bimodal solvent to better understand the factors determining the anti-precipitation action of coil-crystalline block copolymers. We assume an Alexander-de Gennes brush model for the strongly stretched corona chains and explicitly account for the polydispersity of the solvent chains. For the thermodynamic distribution of solvent chains in the corona, we find a predominance of short solvent chains to long solvent chains in the corona phase compared to the solvent bath, both with and without nematic interactions in the corona phase. We also calculate the rate of crystallization of the long solvent chains onto the micellar crystal core and find that the rate is sensitive to both brush and core parameters. In particular, we predict that to maximize the rate, both E fold /kTN A and X n need to be made as small as possible, where E fold is the folding energy of the crystal core chains, N A the number of statistical segments of the solvated corona chains and X n parameterises the strength of nematic interactions in the micellar corona. This leads to the surprising result that for fixed E fold , the rate of crystallization is increased when we increase the molecular weight of the corona blocks.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"35 1","pages":"1379-1392"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90967175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We report rotation of a single director in a nematic monodomain, acrylate based side-chain elastomer which was subjected to mechanical fields applied at angles in the range 80° 90° to the director, no, present at the time of network formation. Time and spatially resolving wide angle X-ray scattering, together with polarised light microscopy measurements revealed a pronounced, almost discontinuous switching mode at a critical extension as the strain was applied at angles approaching 90° to no, whereas a more continuous rotation was seen when the strain was applied at more acute angles. This director reorientation was more or less uniform across the complete sample and was accompaniecl by a modest decrease in orientation parameter (P2). At strains sufficient to induce switching there was some continuous distribution of director orientations with fluctuations of +10° although there was no evidence for any localised director inhomogenities such as domain formation. The observed deformation behaviour of these acrylate-based nematic monodomains was in accord with the predictions of a theory developed by Bladon et al., in that the complete set of data could be accounted for through a single parameter describing the chain anisotropy. The experimentally deduced chain anisotropy parameter was in broad agreement with that obtained from small-angle neutron scattering procedures, but was somewhat greater than that obtained by spontaneous shape changes at the nematic-isotropic transition.
{"title":"A Single Director Switching Mode for Monodomain Liquid Crystal Elastomers","authors":"P. M. Roberts, G. Mitchell, F. Davis","doi":"10.1051/JP2:1997190","DOIUrl":"https://doi.org/10.1051/JP2:1997190","url":null,"abstract":"We report rotation of a single director in a nematic monodomain, acrylate based side-chain elastomer which was subjected to mechanical fields applied at angles in the range 80° 90° to the director, no, present at the time of network formation. Time and spatially resolving wide angle X-ray scattering, together with polarised light microscopy measurements revealed a pronounced, almost discontinuous switching mode at a critical extension as the strain was applied at angles approaching 90° to no, whereas a more continuous rotation was seen when the strain was applied at more acute angles. This director reorientation was more or less uniform across the complete sample and was accompaniecl by a modest decrease in orientation parameter (P2). At strains sufficient to induce switching there was some continuous distribution of director orientations with fluctuations of +10° although there was no evidence for any localised director inhomogenities such as domain formation. The observed deformation behaviour of these acrylate-based nematic monodomains was in accord with the predictions of a theory developed by Bladon et al., in that the complete set of data could be accounted for through a single parameter describing the chain anisotropy. The experimentally deduced chain anisotropy parameter was in broad agreement with that obtained from small-angle neutron scattering procedures, but was somewhat greater than that obtained by spontaneous shape changes at the nematic-isotropic transition.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"16 1","pages":"1337-1351"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77358499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A phenomenological theory is developed for static and dynamic aspects ofsurface- induced ordering of symmetrical block copolymers taking fluctuation corrections into account, but, considering conditions where the bulk block copolymer melt is still disordered, and a lin- earized version of the resulting Ginzburg-Landau type equation suffices. Both the semi-infinite geometry and symmetrical films of thickness 2L are treated, applying the same boundary con- ditions as used previously for a treatment of wetting in polymer blends, assuming short range surface forces and a long Wavelength approximation. For the static order parameter profile in thin film geometry, We derive an oscillatory convergence of both amplitude and phase to the corre- sponding properties of the semi-infinite systems, because terms of order exp(-2L/f+) cos(2Lq*) enter, f+ being the correlation length and = 21r/q* the Wave~length of lamellar ordering. It is shown that the conservation of the number of monomers of the two species, Which can be expressed as a global constraint on the order parameter, leads to a non-linear equation for the phase expressed in terms of the amplitude, When one considers the kinetics of ordering. Both numerical and approximate analytical treatments are given to describe the evolution of the considered systems towards equilibrium.
{"title":"Surface Effects on Block Copolymer Melts Above the Order-Disorder Transition: Linear Theory of Equilibrium Properties and the Kinetics of Surface-Induced Ordering","authors":"K. Binder, Harry L. Risch, S. Stepanow","doi":"10.1051/JP2:1997191","DOIUrl":"https://doi.org/10.1051/JP2:1997191","url":null,"abstract":"A phenomenological theory is developed for static and dynamic aspects ofsurface- induced ordering of symmetrical block copolymers taking fluctuation corrections into account, but, considering conditions where the bulk block copolymer melt is still disordered, and a lin- earized version of the resulting Ginzburg-Landau type equation suffices. Both the semi-infinite geometry and symmetrical films of thickness 2L are treated, applying the same boundary con- ditions as used previously for a treatment of wetting in polymer blends, assuming short range surface forces and a long Wavelength approximation. For the static order parameter profile in thin film geometry, We derive an oscillatory convergence of both amplitude and phase to the corre- sponding properties of the semi-infinite systems, because terms of order exp(-2L/f+) cos(2Lq*) enter, f+ being the correlation length and = 21r/q* the Wave~length of lamellar ordering. It is shown that the conservation of the number of monomers of the two species, Which can be expressed as a global constraint on the order parameter, leads to a non-linear equation for the phase expressed in terms of the amplitude, When one considers the kinetics of ordering. Both numerical and approximate analytical treatments are given to describe the evolution of the considered systems towards equilibrium.","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"7 1","pages":"1353-1378"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76272578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stable standing wave localized solutions of square symmetry are possible for a quintic Swift-Hohenberg type equation with complex coefficients. We point out that these localized solutions, which are surrounded by a pattern-free state exist for a range of values for the external stress parameter subcritically. We discuss similarities to recent experimental observations of standing wave localized squares in granular materials
{"title":"Standing Wave Localized Squares in Pattern-Forming Nonequilibrium Systems","authors":"H. Sakaguchi, H. Brand","doi":"10.1051/JP2:1997188","DOIUrl":"https://doi.org/10.1051/JP2:1997188","url":null,"abstract":"Stable standing wave localized solutions of square symmetry are possible for a quintic Swift-Hohenberg type equation with complex coefficients. We point out that these localized solutions, which are surrounded by a pattern-free state exist for a range of values for the external stress parameter subcritically. We discuss similarities to recent experimental observations of standing wave localized squares in granular materials","PeriodicalId":14774,"journal":{"name":"Journal De Physique Ii","volume":"28 1","pages":"1325-1330"},"PeriodicalIF":0.0,"publicationDate":"1997-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87128400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：