We present an exact calculation of the effective geometry-induced quantum potential for a particle confined on a helicoidal ribbon. This potential leads to the appearance of localized states at the rim of the helicoid. In this geometry the twist of the ribbon plays the role of an effective transverse electric field on the surface and thus this is reminiscent of the Hall effect.The interplay of geometry and topology is a recurring theme in physics, particularly when these effects manifest themselves in unusual electronic and magnetic properties of materials. Specifically, helical ribbons provide a fertile playground for such effects. Both the helicoid ͑a minimal surface͒ and helical ribbons are ubiquitous in nature: they occur in biology, e.g., as beta sheets in protein structures, 1 macromolecules ͑such as DNA͒, 2 and tilted chiral lipid bilayers. 3 Many structural motifs of biomolecules result from helical arrangements: 4 cellulose fibrils in cell walls of plants, chitin in arthropod cuticles, and collagen protein in skeletal tissue.Condensed matter examples include screw dislocations in smectic A liquid crystals 5 and certain ferroelectric liquid crystals. 6 A helicoid to spiral ribbon transition 7 and geometrically induced bifurcations from the helicoid to the catenoid 8 have also been studied.In this context, our goal is to answer the following questions: what kind of an effective quantum potential does a charge ͑or electron͒ experience on a helicoid or a helical ribbon due to its geometry ͑i.e., curvature and twist͒? If the outer edge of the helicoid is charged, how is this potential modified and if there are any bound states? Our main findings are: the twist will push the electrons in vanishing angular-momentum state toward the inner edge of the ribbon and push the electrons in nonvanishing angular-momentum states to the outer edge, thus creating an inhomogeneous effective electric field between the inner and outer rims of the helicoidal ribbon. This is reminiscent of the Hall effect; only here it is geometrically induced. We expect our results to lead to new experiments on related twisted materials where the predicted effect can be verified. In a related context we note that de Gennes 9 had explained the buckling of a flat solid ribbon in terms of the ferroelectric polarization charges on the edges.In order to answer the questions posed above, here we study the helicoidal surface to gain a broader understanding of the interaction between quantum particles and curvature, and the resulting possible physical effects. The properties of free electrons on this geometry have been considered before. 10 The results of this Brief Report are based on the Schrödinger equation for a confined quantum particle on a submanifold of R 3 . Following da Costa 11 an effective potential appears in the two-dimensional Schrödinger equation which has the following form:where m ‫ء‬ is the effective mass of the particle, ប is the Planck's constant, and M and K are the mean and the Gaussian curvature, respectively.To describe the geo...

It is shown that for monolayer graphene electrons are confined on a perfect two dimensional surface. The implications for the electronic properties of corrugated graphene are discussed in view of a derivation of the constrained relativistic dynamics for the massless carriers in two dimensions. Surface curvature is related to a series of phenomena with practical applications such as curvature induced p-n junctions, band gap opening and decoherence. We also establish a bending free energy by treating graphene as a soft electronic membrane.

Natural products have long played a major role in medicine and science. The garden snail Cornu aspersum is a rich source of biologically active natural substances that might be an important source for new drugs to treat human disease. Based on our previous studies, nine fractions containing compounds with Mw <3 kDa; <10 kDa; <20 kDa; >20 kDa; >30 kDa>50 kDa and between 3 and 5 kDa; 5 and 10 kDa; and 10 and 30 kDa were purified from the mucus of C. aspersum and analyzed by tandem mass spectrometry (MALDI-TOF/TOF). Seventeen novel peptides with potential antibacterial activity were identified by de novo MS/MS sequencing using tandem mass spectrometry. The different fractions were tested for antibacterial activity against Gram─ (Pseudomonas aureofaciens and Escherichia coli) and Gram+ (Brevibacillus laterosporus) bacterial strains as well the anaerobic bacterium Clostridium perfringens. These results revealed that the peptide fractions exhibit a predominant antibacterial activity against B. laterosporus; the fraction with Mw 10–30 kDa against E. coli; another peptide fraction <20 kDa against P. aureofaciens; and the protein fraction >20 kDa against the bacterial strain C. perfringens. The discovery of new antimicrobial peptides (AMPs) from natural sources is of great importance for public health due to the AMPs’ effective antimicrobial activities and low resistance rates.