Temporal Dynamics of Adverse Effects across Five Sessions of Transcranial Direct Current Stimulation.

(1) Background: Transcranial direct current stimulation (tDCS) is a safe intervention, only producing mild and transient adverse effects (AEs). However, there is no detailed analysis of the pattern of adverse effects in an application transferable to the clinic. Therefore, our objective is to describe the AEs produced by tDCS and its temporal evolution. (2) Methods: A total of 33 young volunteers were randomized into a tDCS or sham group. Participants performed a hand dexterity task while receiving the tDCS or sham intervention (20 min and 1 mA), for five consecutive days. AEs were assessed daily after each intervention and classified as somatosensory, pain, or other effects. (3) Results: The number of AEs was generally increased by tDCS intervention. Specifically, tDCS led to more frequent somatosensory discomfort, characterized by sensations like itching and tingling, alongside painful sensations such as burning, compared to the sham intervention. Additionally, certain adverse events, including neck and arm pain, as well as dizziness and blurry vision, were exclusive to the tDCS group. Interestingly, tDCS produced similar AEs across the days; meanwhile, the somatosensory AEs in the sham group showed a trend to decrease. (4) Conclusions: tDCS produces mild and temporary somatosensory and pain AEs during and across sessions. The different evolution of the AEs between the tDCS and sham protocol could unmask the blinding protocol most used in tDCS studies. Potential solutions for improving blinding protocols for future studies are discussed.

Ocular surface information seen from the somatosensory thalamus and cortex.

Ocular Surface (OS) somatosensory innervation detects external stimuli producing perceptions, such as pain or dryness, the most relevant symptoms in many OS pathologies. Nevertheless, little is known about the central nervous system circuits involved in these perceptions, and how they integrate multimodal inputs in general. Here, we aim to describe the thalamic and cortical activity in response to OS stimulation of different modalities. Electrophysiological extracellular recordings in anaesthetized rats were used to record neural activity, while saline drops at different temperatures were applied to stimulate the OS. Neurons were recorded in the ophthalmic branch of the trigeminal ganglion (TG, 49 units), the thalamic VPM-POm nuclei representing the face (Th, 69 units) and the primary somatosensory cortex (S1, 101 units). The precise locations for Th and S1 neurons receiving OS information are reported here for the first time. Interestingly, all recorded nuclei encode modality both at the single neuron and population levels, with noxious stimulation producing a qualitatively different activity profile from other modalities. Moreover, neurons responding to new combinations of stimulus modalities not present in the peripheral TG subsequently appear in Th and S1, being organized in space through the formation of clusters. Besides, neurons that present higher multimodality display higher spontaneous activity. These results constitute the first anatomical and functional characterization of the thalamocortical representation of the OS. Furthermore, they provide insight into how information from different modalities gets integrated from the peripheral nervous system into the complex cortical networks of the brain. KEY POINTS: Anatomical location of thalamic and cortical ocular surface representation. Thalamic and cortical neuronal responses to multimodal stimulation of the ocular surface. Increasing functional complexity along trigeminal neuroaxis. Proposal of a new perspective on how peripheral activity shapes central nervous system function.

Nasal Obstruction: Overview of Pathophysiology and Presentation of a Clinically Relevant Preoperative Plan for Rhino(Septo)plasty.

Impairment of nasal breathing is a highly prevalent and bothersome symptom that affects daily functioning and/or sleep quality. Those surgeons dealing with patients seeking rhinoplasty need to carefully analyze the preoperative nasal breathing capacity and predict the positive or even negative impact of rhino(septo)plasty on nasal breathing. Given the lack of correlation between the subjective feeling of suboptimal nasal breathing and the objective measurements of nasal flow and nasal resistance, a critical and mainly clinical evaluation of all anatomical, mucosal, and sensory mechanisms involved in nasal obstruction is mandatory. Indeed, thermo-, mechano-, and chemosensory receptors on the nasal mucosa, airflow, and respiratory dynamics might all contribute to the overall perception of nasal breathing capacity. In this review, we provide an overview of the factors determining suboptimal nasal breathing including different diagnostic and experimental tests that can be performed to evaluate nasal flow and nasal resistance and current limitations in our understanding of the problem of nasal breathing in an individual patient. An algorithm for the preoperative or diagnostic workup for nasal obstruction is included that might be useful as a guide for clinicians dealing with patients seeking nose surgery.

Blood flow effects of percutaneous peripheral nerve stimulation. A blinded, randomized clinical trial.

BACKGROUND: The vasculature function is mainly regulated by the autonomic nervous system. Importantly, the sensory-motor nervous system also innervates peripheral vessels and has the capacity to modulate vascular tone. Here we investigated the effects of electrical stimulation of a mixed nerve trunk on blood flow in deep arteries and muscle perfusion. Our hypothesis is that stimulation of a mixed nerve can modify blood flow. METHODS: Twenty-nine healthy participants were included into a randomized-crossover and blinded clinical trial. Each subject received a placebo and two percutaneous peripheral nerve stimulation (pPNS) protocols on the median nerve: Pain Threshold continuous Low Frequency (PT-cLF) and Sensory Threshold burst High Frequency (ST-bHF). Blood flow was then assessed bilaterally using Power Doppler Ultrasonography at the main arteries of the arm, and blood perfusion at the forearm muscles. Afterwards, blood flow was quantified using a semi-automatized software, freely shared here. RESULTS: Placebo, consisting in needle insertion, produced an immediate and generalized reduction on peak systolic velocity in all arteries. Although nerve stimulation produced mainly no effects, some significant differences were found: both protocols increased the relative perfusion area of the forearm muscles, the ST-bHF protocol prevented the reduction in peak systolic velocity and TAMEAN of the radial artery produced by the control protocol and PT-cLF produced a TAMEAN reduction of the ulnar artery. CONCLUSIONS: Therefore, the arterial blood flow in the arm is mainly impervious to the electrical stimulation of the median nerve, composed by autonomic and sensory-motor axons, although it produces mild modifications in the forearm muscles perfusion.

The Contribution of TRPA1 to Corneal Thermosensitivity and Blink Regulation in Young and Aged Mice.

The role of TRPA1 in the thermosensitivity of the corneal cold thermoreceptor nerve endings was studied in young and aged mice. The contribution of the TRPA1-dependent activity to basal tearing and thermally-evoked blink was also explored. The corneal cold thermoreceptors' activity was recorded extracellularly in young (5-month-old) and aged (18-month-old) C57BL/6WT (WT) and TRPA1-/- knockout (TRPA1-KO) mice at basal temperature (34 °C) and during cooling (15 °C) and heating (45 °C) ramps. The blink response to cold and heat stimulation of the ocular surface and the basal tearing rate were also measured in young animals using orbicularis oculi muscle electromyography (OOemg) and phenol red threads, respectively. The background activity at 34 °C and the cooling- and heating-evoked responses of the cold thermoreceptors were similar in WT and TRPA1-KO animals, no matter the age. Similar to the aged WT mice, in the young and aged TRPA1-KO mice, most of the cold thermoreceptors presented low frequency background activity, a low cooling threshold, and a sluggish response to heating. The amplitude and duration of the OOemg signals correlated with the magnitude of the induced thermal change in the WT but not in the TRPA1-KO mice. The basal tearing was similar in the TRPA1-KO and WT mice. The electrophysiological data suggest that the TRPA1-dependent nerve activity, which declines with age, contributes to detecting the warming of the ocular surface and also to integrating the thermally-evoked reflex blink.

Prediction of the liquid-crystal phase behavior of hard right triangles from fourth-virial density-functional theories.

We have used an extended scaled-particle theory that incorporates four-body correlations through the fourth-order virial coefficient to analyze the orientational properties of a fluid of hard right isosceles triangles. This fluid has been analyzed by computer simulation studies, with clear indications of strong octatic correlations present in the liquid-crystal phase, although the more symmetric order tetratic phase would seem to be the most plausible candidate. Standard theories based on the second virial coefficient are unable to reproduce this behavior. Our extended theory predicts that octatic correlations, associated to a symmetry under global rotations of the oriented fluid by 45^{∘}, are highly enhanced, but not enough to give rise to a thermodynamically stable phase with strict octatic symmetry. We discuss different scenarios to improve the theoretical understanding of the elusive octatic phase in this intriguing fluid.

Effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids.

We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schulz distribution function. We implemented the scaled particle theory for this model with the aim of studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid and (ii) how polydispersity affects phase transitions between isotropic, nematic, and tetratic phases. We found that roundness greatly affects the tetratic phase, whose region of stability in the phase diagram strongly decreases as the roundness parameter is increased. Also, the interval of aspect ratios where the tetratic-nematic and isotropic-nematic phase transitions are of first order considerably reduces with roundness, both transitions becoming weaker. Polydispersity induces strong fractionation between the coexisting phases, with the nematic phase enriched in particles of lower roundness. Finally, for high enough polydispersity and certain mean aspect ratios, the isotropic-to-nematic transition can change from second (for the one-component fluid) to first order. We also found a packing-fraction inversion phenomenon for large polydispersities: the coexisting isotropic phase has a higher packing fraction than the nematic.

Endogenous Pain Modulation in Response to a Single Session of Percutaneous Electrolysis in Healthy Population: A Double-Blinded Randomized Clinical Trial.

The purpose of this double-blinded randomized controlled trial was to investigate whether percutaneous electrolysis (PE) is able to activate endogenous pain modulation and whether its effects are dependent on the dosage of the galvanic current. A total of 54 asymptomatic subjects aged 18-40 years were randomized into three groups, receiving a single ultrasound-guided PE intervention that consisted of a needle insertion on the lateral epicondyle tendon: sham (without electrical current), low-intensity (0.3 mA, 90 s), and high-intensity (three pulses of 3 mA, 3 s). Widespread pressure pain thresholds (PPT), conditioned pain modulation (CPM), and temporal summation (TS) were assessed in the elbow, shoulder, and leg before and immediately after the intervention. Both high and low intensity PE protocols produced an increase in PPT in the shoulder compared to sham (p = 0.031 and p = 0.027). The sham group presented a significant decrease in the CPM (p = 0.006), and this finding was prevented in PE groups (p = 0.043 and p = 0.025). In addition, high-intensity PE decreased TS respect to sham in the elbow (p = 0.047) and both PE groups reduced TS in the leg (p = 0.036 and p = 0.020) without significant differences compared to sham (p = 0.512). Consequently, a single PE intervention modulated pain processing in local and widespread areas, implying an endogenous pain modulation. The pain processing effect was independent of the dosage administrated.

Epithelial and sensory mechanisms of nasal hyperreactivity.

"Nasal hyperreactivity" is a key feature in various phenotypes of upper airway diseases, whereby reactions of the nasal epithelium to diverse chemical and physical stimuli are exacerbated. In this review, we illustrate how nasal hyperreactivity can result from at least three types of mechanisms: (1) impaired barrier function, (2) hypersensitivity to external and endogenous stimuli, and (3) potentiation of efferent systems. We describe the known molecular basis of hyperreactivity related to the functional impairment of epithelial cells and somatosensory innervation, and indicate that the thermal, chemical, and mechanical sensors determining hyperreactivity in humans remain to be identified. We delineate research directions that may provide new insights into nasal hyperreactivity associated with rhinitis/rhinosinusitis pathophysiology and therapeutics. The elucidation of the molecular mechanisms underlying nasal hyperreactivity is essential for the treatment of rhinitis according to the precepts of precision medicine.

A genetic compensatory mechanism regulated by Jun and Mef2d modulates the expression of distinct class IIa Hdacs to ensure peripheral nerve myelination and repair.

The class IIa histone deacetylases (HDACs) have pivotal roles in the development of different tissues. Of this family, Schwann cells express Hdac4, 5, and 7 but not Hdac9. Here, we show that a transcription factor regulated genetic compensatory mechanism within this family of proteins, blocks negative regulators of myelination ensuring peripheral nerve developmental myelination and remyelination after injury. Thus, when Hdac4 and 5 are knocked-out from Schwann cells in mice, a JUN-dependent mechanism induces the compensatory overexpression of Hdac7 permitting, although with a delay, the formation of the myelin sheath. When Hdac4, 5, and 7 are simultaneously removed, the myocyte-specific enhancer-factor d (MEF2D) binds to the promoter and induces the de novo expression of Hdac9, and although several melanocytic lineage genes are misexpressed and Remak bundle structure is disrupted, myelination proceeds after a long delay. Thus, our data unveil a finely tuned compensatory mechanism within the class IIa Hdac family, coordinated by distinct transcription factors, that guarantees the ability of Schwann cells to myelinate during development and remyelinate after nerve injury.

Membrane potential instabilities in sensory neurons: mechanisms and pathophysiological relevance.

ABSTRACT: Peripheral sensory neurons transduce physicochemical stimuli affecting somatic tissues into the firing of action potentials that are conveyed to the central nervous system. This results in conscious perception, adaptation, and survival, but alterations of the firing patterns can result in pain and hypersensitivity conditions. Thus, understanding the molecular mechanisms underlying action potential firing in peripheral sensory neurons is essential in sensory biology and pathophysiology. Over the past 30 years, it has been consistently reported that these cells can display membrane potential instabilities (MPIs), in the form of subthreshold membrane potential oscillations or depolarizing spontaneous fluctuations. However, research on this subject remains sparse, without a clear conductive thread to be followed. To address this, we here provide a synthesis of the description, molecular bases, mathematical models, physiological roles, and pathophysiological implications of MPIs in peripheral sensory neurons. Membrane potential instabilities have been reported in trigeminal, dorsal root, and Mes-V ganglia, where they are believed to support repetitive firing. They are proposed to have roles also in intercellular communication, ectopic firing, and responses to tonic and slow natural stimuli. We highlight how MPIs are of great interest for the study of sensory transduction physiology and how they may represent therapeutic targets for many pathological conditions, such as acute and chronic pain, itch, and altered sensory perceptions. We identify future research directions, including the elucidation of the underlying molecular determinants and modulation mechanisms, their relation to the encoding of natural stimuli and their implication in pain and hypersensitivity conditions.

Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles.

A fluid of hard right isosceles triangles was studied using an extension of scaled-particle density-functional theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal phase predicted by the theory is the uniaxial nematic phase, in agreement with the second-order virial theory. By contrast, Monte Carlo simulations predict exotic liquid-crystal phases exhibiting tetratic and octatic correlations, with orientational distribution functions having four and eight equivalent peaks, respectively. This demonstrates the failure of the standard density-functional theory based on two- and three-body correlations to describe high-symmetry orientational phases in two-dimensional hard right-triangle fluids, and it points to the necessity to reformulate the theory to take into account high-order body correlations and ultimately particle self-assembling and clustering effects. This avenue may represent a great challenge for future research, and we discuss some fundamental ideas to construct a modified version of density-functional theory to account for these clustering effects.

Deciphering the Action of Perfluorohexyloctane Eye Drops to Reduce Ocular Discomfort and Pain.

Perfluorohexyloctane (F6H8) eyedrops have been recently introduced in Europe as a product to treat dry eye disease, based on its ability to reduce tear film instability in Meibomian gland dysfunction and evaporative dry eye disease, although its mechanism of action is still unknown. In the present pilot study, we evaluated the effects of the ocular instillation of a single drop of commercial F6H8 eyedrops in 20 healthy humans (9 women/11 men), measuring: (a) Corneal surface temperature (CST) from infrared video images; (b) tear volume using phenol red threads; (c) blinking frequency; and (d) ocular surface sensations (cold, dryness, pricking, foreign body, burning, itching, gritty, eye fatigue, watering eyes, and light-evoked discomfort sensations; scored using 10 cm Visual Analog Scales), before and 5-60 min after F6H8 or saline treatment. CST decreased and tearing and blinking frequency increased significantly after F6H8 but not after saline solution. When applied unilaterally, CST decreased only in the F6H8-treated eye. No sensations were evoked after F6H8 or saline. The corneal surface temperature reduction produced by topical F6H8 does not evoke conscious ocular sensations but is sufficient to increase the activity of corneal cold thermoreceptors, leading to an increased reflex lacrimation and blinking that may relieve dry eye condition thus reducing ocular discomfort and pain.

Effects of Percutaneous Electrolysis on Endogenous Pain Modulation: A Randomized Controlled Trial Study Protocol.

Percutaneous electrolysis consists of the application of a galvanic electrical current throughout an acupuncture needle. It has been previously hypothesized that needling procedures' neurophysiological effects may be related to endogenous pain modulation (EPM). This protocol study describes the design of a double-blind (participant, assessor) randomized controlled trial with the aim to investigate whether percutaneous electrolysis is able to enhance EPM and whether the effect is different between two applications depending on the dosage of the galvanic electrical current. Seventy-two asymptomatic subjects not reporting the presence of pain symptoms the previous 6 months before the study, aged 18-40 years, are randomized into one of four groups: a control group who does not receive any intervention, a needling group who receives a needling intervention without electrical current, a low-intensity percutaneous electrolysis group (0.3 mA × 90 s), and a high-intensity percutaneous electrolysis group (three bouts of 3 mA × 3 s). Needling intervention consists of ultrasound-guided insertion of the needle on the common extensor tendon of the lateral epicondyle. The primary outcome is conditioned pain modulation (CPM), and secondary outcomes include widespread pressure pain sensitivity (pressure pain thresholds (PPT) over the lateral epicondyle, the cervical spine, and the tibialis anterior muscle) and temporal summation (TS). We expected that percutaneous electrolysis would have a greater influence on CPM than an isolated needling procedure and no intervention. In addition, we also postulated that there might be differences in outcome measures depending on the intensity of the electrical current during the percutaneous electrolysis application. This study makes a new contribution to the field of neurophysiological effects of percutaneous electrolysis and needling interventions.

Reversed Polarity bi-tDCS over M1 during a Five Days Motor Task Training Did Not Influence Motor Learning. A Triple-Blind Clinical Trial.

Transcranial direct current stimulation (tDCS) has been investigated as a way of improving motor learning. Our purpose was to explore the reversal bilateral tDCS effects on manual dexterity training, during five days, with the retention component measured after 5 days to determine whether somatosensory effects were produced. In this randomized, triple-blind clinical trial, 28 healthy subjects (14 women) were recruited and randomized into tDCS and placebo groups, although only 23 participants (13 women) finished the complete protocol. Participants received the real or placebo treatment during five consecutive days, while performing a motor dexterity training program of 20 min. The motor dexterity and the sensitivity of the hand were assessed pre- and post-day 1, post 5 days of training, and 5 days after training concluded. Training improved motor dexterity, but tDCS only produced a tendency to improve retention. The intervention did not produce changes in the somatosensory variables assessed. Thus, reversal bi-tDCS had no effects during motor learning on healthy subjects, but it could favor the retention of the motor skills acquired. These results do not support the cooperative inter-hemispheric model.

Static magnetic stimulation in the central nervous system: a systematic review.

OBJECTIVE: To systematically review the literature on the use of the transcranial static magnetic stimulation (tSMS) technique in humans and animals, its effects on different areas of the central nervous system (CNS), its influence on neural excitability and on the subject's behavior, and its biological effects and future possibilities. All static magnetic field applications that can be considered to have a physiologically similar effect have been reviewed. METHODS: We searched studies using key terms in NCBI PubMed, Scopus, PEDro, SciELO, Cochrane, and links to publications (inception to September 2019). Three reviewers independently selected the studies, extracted data, and assessed the methodological quality of the studies using the recommendations described in the Cochrane Handbook for Systematic Reviews of Interventions, PRISMA guidelines. RESULTS: We analyzed 27 studies. The reviewed literature suggests that the use of these magnetic fields has an inhibitory effect on different areas of the CNS, such as motor, somatosensory, and visual cortex, cerebellum, and spinal cord. Regarding subject's behavior, the different effects of tSMS appear to be transient and dependent on the stimulated area, such as loss of visual discrimination or improvement of somatosensory perception. In addition, the technique has some therapeutic utility, specifically in pathologies with cortical hyperexcitability. CONCLUSIONS: These results suggest that tSMS may be a promising tool to modulate cerebral excitability in a safe and non-invasive way. Further investigations could give a better explanation of its precise mechanisms of action and applications.

Orientational ordering in a fluid of hard kites: A density-functional-theory study.

Using density-functional theory we theoretically study the orientational properties of uniform phases of hard kites-two isosceles triangles joined by their common base. Two approximations are used: scaled particle theory and a new approach that better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters, kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus, a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic, and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to 90^{∘}, 60^{∘}, and 75^{∘}. Kites with one of their unequal angles fixed to 72^{∘}, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilize the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to 60^{∘} stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to 75^{∘} have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally, the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to 72^{∘}. These particles also present a phase diagram with stable tetratic and triatic phases.

Solitary extrapleural fibrous tumor with hepatic bilobar metastases: multimodal approach treatment.

BACKGROUND: Solitary fibrous tumor is an unusual fibroblastic mesenchymal neoplasm typically described in the pleura. It may appear anywhere with a varied anatomic distribution and essentially it can develop from any soft tissue or visceral location. Its course is usually indolent and it rarely causes distant metastases, so it has a prolonged survival rate. It sometimes presents itself as a disseminate disease being the liver the most frequently involved location. In these occasions, the management should be discussed in a multidisciplinary tumor committee formed by surgeons, oncologists and radiologists. Surgery remains the gold standard for treatment. CASE REPRESENTATION: We present the case of a woman with a tumor in the left abdominal wall and bilobar massive liver metastases, both locations histologically diagnosed as solitary fibrous tumor. She receives biological treatment for a severe case of Crohn´s disease. Evaluated in a multidisciplinary committee, surgery was recommended for both the primary lesion and the liver metastases. The hepatobiliary surgeons considered a two-stage hepatectomy with portal vein embolization (PVE) as the best strategy. After the first procedure consisting in cleaning the left hepatic lobe followed by PVE the future liver remnant volume (FLRV) was considered inadequate, so the patient was also treated with right transarterial radioembolizacion with yttrium 90 (TARE-Y90) intending a double goal: to treat the tumor and to increased the FLRV. Furthermore, a severe flare of Crohn´s disease forced us to intensify the patient's treatment with the addition of biological agents (infliximab and adalimumab) until complete remission of the symptoms. The second stage of the liver surgery had to be postponed for more than 6 months and could finally be carried out without complications, achieving an R0 resection. The postoperative course was uneventful and the follow up has showed no recurrence to date. CONCLUSION: Solitary fibrous tumours with extensive liver metastases are infrequent but when they appear modern surgical strategies like two stage hepatectomy are the treatment of choice and must be carried out by specialised units. The therapeutic decisions should be guided by a multidisciplinary committee.

Highly confined mixtures of parallel hard squares: A density-functional-theory study.

Using the fundamental-measure density-functional theory, we study theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting of two consecutive big squares, or three small squares, in the transverse direction, perpendicular to the walls, are forbidden. We analyze two different mixtures with edge lengths of species selected so as to allow or forbid one big plus one small square to fit into the channel. For the first mixture we obtain first-order transitions between symmetric and asymmetric packings of particles: Small and big squares are preferentially adsorbed at different walls. Asymmetric configurations are shown to lead to more efficient packing at finite pressures. We argue that the stability region of the asymmetric phase in the pressure-composition plane is bounded so that the symmetric phase is stable at low and very high pressure. For the second mixture, we observe strong demixing between phases which are rich in different species. Demixing occurs in the lateral direction, i.e., the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behavior (which in practical terms is precluded by jamming) in strictly two-dimensional systems is discussed. Finally, the phase behavior of a mixture with periodic boundary conditions is analyzed and the differences and similarities between the latter and the confined system are discussed. We claim that, although exact calculations exclude the existence of true phase transitions in (1+ε)-dimensional systems, density-functional theory is still successful in describing packing properties of large clusters of particles.

Uniform phases in fluids of hard isosceles triangles: One-component fluid and binary mixtures.

We formulate the scaled particle theory for a general mixture of hard isosceles triangles and calculate different phase diagrams for the one-component fluid and for certain binary mixtures. The fluid of hard triangles exhibits a complex phase behavior: (i) the presence of a triatic phase with sixfold symmetry, (ii) the isotropic-uniaxial nematic transition is of first order for certain ranges of aspect ratios, and (iii) the one-component system exhibits nematic-nematic transitions ending in critical points. We found the triatic phase to be stable not only for equilateral triangles but also for triangles of similar aspect ratios. We focus the study of binary mixtures on the case of symmetric mixtures: equal particle areas with aspect ratios (κ_{i}) symmetric with respect to the equilateral one, κ_{1}κ_{2}=3. For these mixtures we found, aside from first-order isotropic-nematic and nematic-nematic transitions (the latter ending in a critical point): (i) a region of triatic phase stability even for mixtures made of particles that do not form this phase at the one-component limit, and (ii) the presence of a Landau point at which two triatic-nematic first-order transitions and a nematic-nematic demixing transition coalesce. This phase behavior is analogous to that of a symmetric three-dimensional mixture of rods and plates.